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EFFICIENCY 
ARITHMETIC 

ADVANCED 


BY 

CHARLES  E.  CHADSEY,  Ph.  D. 

DEAN  OF  COLLEGE  OF  EDUCATION, 

UNIVERSITY  OF  ILLINOIS,  URBANA, 

ILL.,  FORMERLY  SUPERINTENDENT 

OF  SCHOOLS.  DETROIT.  MICH. 

AND 

JAMES  H.  SMITH,  A.  M. 

SUPERINTENDENT    OF    SCHOOLS. 
BELVIDERE,    ILL.,   FORMERLY    IN- 
STRUCTOR   IN    MATHEMATICS. 
SCHOOL   OF   EDUCATION 
UNIVERSITY  OF  CHICAGO 


MENTZER,  BUSH  &  COMPANY 

Boston  New  York  Chicago  Dallas 


COPYRIGHT.  1917-1920.  BY 

ATKINSON.  MENTZER  &  COMPANV 

All  rizhts  reserved 


QA 

PREFACE 

This  book  has  been  prepared  in  the  belief  that  work  in 
Arithmetic  in  the  seventh  and  eighth  grades  should  emphasize 
drill  upon  fundamentals  and  their  application  to  living,  vital 
problems  that  the  average  child  is  almost  sure  to  encounter  in 
his  individual  experiences.  At  the  same  time,  it  is  recognized 
that  for  the  great  majority  using  the  books  of  this  series  certain 
topics  will  never  receive  consideration  in  the  school  training 
unless  presented  in  this  volume.  Great  care  has  been  taken  to 
present  these  topics  in  a  simple,  clear  manner  which  ought  to 
make  their  meaning  and  significance  intelligible  even  to  the 
younger  pupils. 

The  problems  of  the  book,  almost  without  exception,  are 
actual  problems  taken  from  the  various  lines  of  business 
represented.  Business  men  from  all  sections  of  the  country 
have  contributed  problems,  furnished  definite  and  accurate 
information  upon  which  to  base  problems,  and  have  criticized 
the  work  from  the  standpoint  of  practical  efficiency  and 
reliability.  Acknowledgment  is  hereby  made  to  these  gentle- 
men for  their  invaluable  assistance. 

The  methods  of  presentation  and  explanation  of  topics  new. 
to  the  child  have  been  carefully  tested  in  the  school  room  and 
their  effectiveness  is  thereby  assured.  Simplicity,  clearness, 
and  the  avoidance  of  unnecessary  repetition  we  believe  to  be 
characteristic  of  this  series,  especially  in  the  applications  of 
percentage  and  practical  measurements  which  so  often  unneces- 
sarily confuse  the  pupil. 

Many  school  systems  are  modifying  their  courses  in  mathe- 
mathics  in  order  to  permit  elementary  algebra  to  be  commenced 
in  the  eighth  grade.  This  volume  permits,  through  its  arrange- 
ment, a  very  simple  omission  of  topics  in  Part  I  which  will 

III 

a485G0 


IV  PREFACE 

enable  any  teacher  to  cover  the  essential  topics  in  less  than 
the  customary  two  years.  The  arrangement  also  enables  those 
who  prefer  to  postpone  some  of  the  topics  found  in  Part  I  to 
combine  the  seventh-  and  eighth-grade  topics  in  such  a  way 
as  to  give  a  more  extended  discussion  of  closely  related  subjects. 

The  fact  that  there  are  in  reality  only  a  few  mathematical 
principles  involved  in  ordinary  arithmetic  is  kept  clearly  in 
mind.  Too  often  the  pupil  has  been  led  to  believe  that  each 
new  topic  has  little  in  common  with  preceding  topics  and 
therefore  fails  to  learn  the  greatest  educational  lesson  that 
can  be  taught — ^the  application  of  a  known  principle  to  a  new 
condition.  The  effort  in  this  book  is  to  keep  the  relationship 
between  mathematical  facts  constantly  before  the  pupil. 

Teachers  of  arithmetic  must  never  forget  that  accuracy  and 
reasonable  rapidity  in  manipulation  of  numbers  are  one  of  the 
chief  aims  in  this  study.  Pupils  of  the  seventh  and  eighth 
grades  need  continued  practice  of  this  kind.  Ample  oppor- 
tunity for  this  drill  is  furnished,  and  from  the  beginning  to  the 
end  of  the  course  there  should  be  recurrence  to  these  exercises. 

While  it  is  not  possible,  in  the  limited  space,  to  make  per- 
sonal acknowledgment  to  the  large  number  of  educators  who 
have  rendered  assistance  of  great  value  in  the  preparation 
of  this  volume,  the  authors  desire  to  express  their  indebted- 
ness especially  to  Miss  Katherine  L.  McLaughlin  of  the 
Department  of  Public  Instruction,  Madison,  Wisconsin,  and 
to  Mr.  James  C.  Thomas  of  the  publishers'  editorial  de- 
partment, for  their  invaluable  criticisms  and  suggestions. 
Credit  is  also  due  to  Mr.  Charles  L,  Spain,  Assistant  Super- 
intendent of  Schools,  Detroit,  Michigan,  for  valuable  help 
relating  to  the  "Speed  and  Accuracy"  drills  given  through- 
out this  series. 


CONTENTS 

/ 

PART  I— SEVENTH  YEAR 

CHAPTER  I.    REVIEW  OF  THE  FUNDAMENTALS— 1-26 
Tkaining  for  Speed  and  Accuracy 

CHAPTER  II.     REVIEW  OF  FRACTIONS— 27-48 

Three  Meanings  of  Fractions,  27  j  Reduction  of  Fractions,  27; 
Addition  and  Subtraction  of  Fractions,  29;  Multiplication  and 
Division  of  Fractions,  33;  Review  of  Decimals,  38;  Applied  Review 
Problems  in  Fractions,  45. 

CHAPTER  III.     PERCENTAGE— 49-88 

Explaining  Per  Cent,  49;  The  Decimal  Point  and  Percentage,  49; 
Common  Fractions  and  Their  Equivalent  Per  Cents,  50;  Equations 
Applied  to  Percentage,  52;  Drill  Problems  in  Percentage,  55; 
Problems  Collected  by  Pupils,  73;  Applied  Problems  in  Percent- 
age, 75. 

CHAPTER    IV.     APPLICATIONS    OF    PERCENTAGE— 89-128 

Business  Transactions,  89;  Discounts,  91;  Interest,  95;  Partial 
Payments,  101;  Commission,  104;  Taxes,  107;  Special  Assessments,  110; 
Custom  Duties,  112;  Internal  Revenue,  115;  Income  Taxes,  116; 
Insurance,  118. 

.     CHAPTER  V.     BUSINESS  FORMS  AND  ACCOUNTS— 129-148 

Sales  Slips,  129;  Invoices,  131;  Monthly  Statements,  133;  Receipts, 
134;  Cash  Accounts,  135;  Daybook  or  Journal,  137;  Personal  Ac- 
counts, 138;  Inventories,  140;  Pay  Rolls,  141;  Cashier's  Memo- 
randum, 142;  Agencies  for  Shipping  Merchandise,  144-6. 

CHAPTER  VI.     PRACTICAL  MEASUREMENTS— 147-170 

Lines  and  Angles,  149;  Rectangles,  151;  Boy  Scouts — Applied 
Problems,  154;  Parallelograms,  156;  Trapezoids,  158;  Triangles,  159; 
Area  of  Triangles,  160;  Constructions  Used  in  Measurements,  163; 
Applied  Problems,  165. 

V 


VI  CONTENTS 

PART  II— EIGHTH  YEAR 

CHAPTER  I.     REVIEW  EXERCISES— 171-198 

Training  for  Efficiency,  171;  Checking  Up,  171;  Speed  Tests  in 
Multiplication,  175;  Short  Methods  in  Multiplication,  176;  Speed 
Tests  in  Division,  180;  Short  Methods  in  Division,  180;  Review  of 
Fractions,  183;  Review  of  Decimals,  185;  Review  of  Percentage,  188. 

CHAPTER  II.     BANKS  AND  BANKING— 199-230 

Bank  Deposits,  200;  Checks,  201;  Savings  Accounts,  204;  Bank 
Discount,  208;  Exchange,  209;  Federal  Reserve  Banks,  214;  Stocks 
AND  Bonds,  216;  Signatures  and  Seals,  221;  Investments,  225. 

CHAPTER  III.     REMITTING  MONEY— 231-238 

Postal  Money  Orders,  231;  Express  Money  Orders,  232;  Bank 
Drafts,  233;  Checks,  234;  Emergency  Remittances,  236;  Telegraph- 
ing Money,  236;  Cabling  Money,  237;  Money  by  Wireless,  238. 

CHAPTER  IV.     PRACTICAL  MEASUREMENTS— 239-281 

Quadrilaterals,  239;  Triangles,  240;  Squares  and  Square  Roots, 
241;  Right  Triangles,  246;  Equilateral  Triangles,  251;  Circles, 
253;  Shop  Problems,  255;  Hexagons,  260;  Solids,  261;  Prisms,  262; 
Cylinders,  268;  Silos,  269;  Irrigation,  270;  Good  Roads,  272. 

CHAPTER  V.     EFFICIENCY  IN  THE  HOME— 282-293 

Building  a  Home,  282;  Furnishing  a  Home,  284;  Expenses  of  a 
Home,  286;  Campfire  Girls,  287;  The  Family  Budget.  288;  Efficiency 
IN  Business,  290. 

CHAPTER  VI.     MEASURING  INSTRUMENTS— 294-312 

Thermometer,  294;  Barometer,  296;  Hygrometer,  297;  Weather 
Reports,  298;  Electric  Meter,  302;  Gas  Meter,  304;  Steam  Gauge, 
306;  Surveyor's  Chain,  307;  Measurement  of  Time,  308;  Standard 
Time,  309;  International  Date  Line,  311. 

CHAPTER  VII.     GRAPHS— 313-319 

Pictorial  Graphs,  313;  Line  Graphs,  314;  Bar  Graphs,  316;  Dis- 
tribution Graphs,  318;  Circle  Graphs,  319. 

CHAPTER  VIII.     THE  METRIC  SYSTEM— 320-329 

Weights  and  Measures,  320;  Lengths,  321;  Square  Measure,  322; 
Volume,  323;  Capacity,  324;  Weight,  325;  Supplement,  332;  Index,  345. 


ADVANCED  ARITHMETIC 

PART   I 
Training  for  Speed  and  Accuracy 


Several  weeks  before  the  opening  of  the  regular  baseball 
season,  the  players  of  the  big  leagues  go  south  for  a  spring 
training  trip.  The  players,  with  their  lack  of  exercise  during 
the  winter's  vacation,  would  not  be  in  proper  condition  to  go 
into  the  opening  game  of  the  season  without  this  sort  of 
preparation. 

You  are  just  returning  from  a  summer's  vacation,  during 
which  you  have  lost  some  of  your  speed  and  accuracy  in  the 
various  processes  of  arithmetic.  It  is  therefore  wise  for  you 
to  take  a  preliminary  training  trip  by  reviewing  the  fundamental 
processes. 

When  asked  what  the  new  workers  in  his  firm  needed  most 
in  arithmetic,  the  head  of  the  school  for  training  workers  in 
one  of  the  largest  mercantile  firms  in  the  country  repUed: 
"Teach  them  to  add,  subtract,  multiply  and  divide."  He 
emphasized  what  all  business  men  want — speed  and  accuracy 
in  those  four  fundamental  processes. 


CHAPTER  I 

REVIEW  EXERCISES 

Exercise  1.    Reading  Numbers 

In  your  studies  and  in  reading  the  magazines  and  daily 
papers  you  are  frequently  called  upon  to  read  numbers.  For 
convenience  in  reading,  large  numbers  are  pointed  off  into 
periods  as  in  the  following  illustration: 


.2      3      3 


III 


6,069,000,000,000,000,000,000. 

The  number  above  represents  the  estimated  weight  of  the 
earth  in  tons.    Read  it. 

In  the  following  table  the  diameter  and  average  distance 
from  the  sun  is  given  for  each  of  the  planets  in  our  solar  system. 
Read  these  distances. 


Name  of 
planet 

Diameter 
in  miles 

Average  distance  from 
the  sun  in  miles 

1.  Mercury 

2,962 

35,392,638 

2.  Venus 

7,510 

66,131,478 

3.  Earth 

7,925 

91,430,220 

4.  Mars 

4,920 

139,312,226 

6.  Jupiter 

88,390 

475,693,149 

6.  Saturn 

77,904 

872,134,583 

7.  Uranus 

33,024 

1,753,851,052 

8.  Neptune 

36,620 

2,746,271,232 

A  rapid  review  of  this  chapter  should  be  given,  followed  by  a  systematic 
use  of  one  or  more  of  the  standardized  drill  exercises  at  the  beginning  of 
each  recitation  period. 

2 


REVIEW  EXERCISES  3 

Exercise  2.    Writing  Numbers 

Occasionally  one  is  called  upon  to  write  difficult  numbers, 
and  he  should  be  able  to  do  so  when  the  need  arises. 

Write  the  following  numbers : 

1.  Ten  thousand  ten. 

2.  One  hundred  fifty  thousand  fifteen. 

3.  Two  million  two  hundred  thousand. 

4.  Sixteen  million  sixteen  thousand  sixteen. 

6.  Twenty-eight  million  four  hundred  fifteen  thousand. 

6.  Two  billion  one  million  two  hundred  thousand  seventy. 

7.  Four  trillion  four  hundred  billion  two  million. 

8.  Sixteen  billion  sixty  million  fifteen  thousand. 

9.  Twenty-four  billion  sixty  million  sixty  thousand. 

10.  Seventy  million  seventeen  thousand  six. 

11.  Twenty-nine  billion  six  million  twenty  thousand. 

12.  Fifty  million  one  hundred  fifty  thousand  thirteen. 

13.  Forty  billion  one  hundred  seventy  million. 

14.  Eight  hundred  thousand  nine  hundred  sixty-four. 

15.  Twenty-four  million  twenty-six  thousand  two  hundred. 


Exercise  3.    Roman  Notation 

It  is  customary  to  express  chapters  of  books  and  often  dates 
on  important  buildings  in  Roman  numerals.  Read  the  following 
numbers : 


1. 

IV 

6.  XIX 

11.  XLIV 

16.  D 

2. 

VI 

7.  XX 

12.  LXVI 

17.  M 

3. 

XIV 

8.  XXII 

13.  XC 

18.  MDC 

4. 

XVI 

9.  XXXIV 

14.  XCVII 

19.  MDCCCXCVII 

6. 

XVIII 

10.  XL 

15.  C 

20.  MDCCCCXVII 

Express  in 

L  Roman  numerals: 

1. 

9 

3.  29 

5.  47 

7.  72                9.  1492 

2. 

14 

4.  33 

6.  58 

8.  96              10.  1918 

4  SEVENTH  YEAR 

EXERCISES  FOR  SPEED  AND  ACCURACY 
Addition,  Subtraction,  Multiplication,  and  Division 

To  the  Teacher:  The  following  exercises  have  been  standardized  so 
that  the  same  time  limits  should  be  used  for  each  exercise.  In  the  prepar- 
ation of  this  drill  material,  all  of  the  fundamental  facts  were  included,  but 
special  emphasis  was  placed  upon  the  diflBcult  facts  by  including  them 
more  frequently  than  the  easy  facts. 

The  following  time  limits  have  been  selected  after  a  careful  study  of 
the  achievements  of  pupils  in  the  cities  where  extensive  surveys  have  been 
made.  The  use  of  the  three  time  limits  provides  an  incentive  for  the  rapid 
workers  in  a  class  as  well  as  the  slow  ones. 


Grade 

Excellent 

Good 

Fair 

Seventh 

1§  minutes 

2    minutes 

2^  minutes 

Eighth 

1    minute 

1^  minutes 

2    minutes 

The  best  results  can  be  obtained  by  giving  one  or  two  of  these  exercises 
at  the  beginning  of  each  arithmetic  recitation.  Most  of  the  exercises  can 
be  conveniently  done  by  placing  a  sheet  of  paper  under  the  examples  in  the 
book  and  writing  the  answers  on  this  sheet  of  loose  paper.  Those  exer- 
cises which  cannot  be  conveniently  done  in  this  manner  should  be  hekto- 
graphed  or  mimeographed. 

These  exercises  may  be  used  in  two  ways: 

(1)  All  pupils  may  practice  on  each  exercise  together.  The  teacher 
should  announce  the  three  time  limits  in  succession,  each  pupil  indicating 
by  E,  G,  or  F  the  time  in  which  he  finished  the  exercise.  After  time  is 
called,  the  pupils  should  exchange  papers  and  check  them  as  the  teacher 
reads  the  correct  answers.  The  teacher  should  keep  individual  records 
of  the  time  limits  made  by  each  pupil,  also  noting  the  number  of  examples 
correctly  worked  by  each  pupil  not  finishing  the  exercise  in  one  of  the  three 
time  limits. 

(2)  Start  all  of  the  pupils  on  the  first  exercise.  As  soon  as  a  pupil 
finishes  correctly  all  of  the  examples  in  this  exercise  in  one  of  the  three 
time  limits,  he  should  go  on  with  the  next  exercise.  Under  this  plan  each 
pupil  can  progress  at  his  own  pace.  Only  the  papers  of  those  who  have 
finished  need  be  collected  and  checked,  because  those  who  did  not  finish 
must  repeat  the  same  exercise.  Do  not  require  a  pupil  to  practice  on  the 
same  exercise  more  than  3  or  4  times,  but  allow  him  to  go  on  and  attempt  at 
a  later  date  to  complete  the  unfinished  exercise. 


EXERCISES  FOR  SPEED  AND  ACCURACY 
Exercise  4.    Addition 


4 

6 

7 

2 

2 

6 

6 

7 

1 

9 

3 

4 

2 

6 

3 

5 

2 

2 

4 

2 

7 

1 

3 

4 

7 

3 

3 

9 

7 

3 

4 

6 

7 

4 

6 

8 

6 

1 

5 

9 

8 

4 

2 

6 

1 

3 

1 

6 

1 

8 

3 

5 

0 

3 

1 

3 

5 

2 

1 

0 

7 

9 

9 

1 

4 

5 

9 

2 

8 

8 

8 

4 

2 

4 

7 

1 

6 

7 

2 

8 

4 

3 

1 

8 

3 

3 

1 

1 

0 

2 

4 

0 

5 

5 

3 

1 

6 

7 

8 

9 

6 

7 

8 

5 

1 

9 

9 

6 

4 

5 

1 

2 

6 

5 

1 

6 

6 

3 

9 

7 

4 

G 

6 

2 

2 

2 

2 

3 

1 

3 

9 

3 

7 

6 

7 

7 

2 

5 

8 

3 

4 

4 

4 

9 

Exercise  5.    Subtraction 


19 

36 

31 

27 

44 

19 

59 

53 

22 

38 

43 

66 

_7 

9 

8 

_3 

J 

4 

2 

JI 

7 

4 

5 

5 

67 

32 

62 

88 

24 

79 

41 

30 

66 

50 

36 

61 

_9 

_3 

_Q 

8 

6 

6 

JI 

_3 

J 

_7 

7 

2 

43 

99 

44 

28 

76 

70 

54 

28 

41 

38 

64 

86 

_6 

8 

3 

9 

2 

4 

_8 

3 

4 

_5 

J 

J 

Exercise  6.    Multiplication 


28 

36 

93 

24 

80 

75 

79 

85 

65 

80 

96 

26 

49 

J 

_7 

^ 

J 

J 

_8 

J 

2 

J 

^ 

3 

6 

2 

19 

57 

38 

64 

73 

47 

56 

61 

67 

80 

14 

49 

38 

J 

_7 

J 

J 

J 

_5 

Ji 

_4 

_2 

J 

^ 

_7_ 

_8 

SEVENTH  YEAR 
Exercise  7.    Division 


2)430  5)895  3)171  2)680  6)474  5)325 


9)756  4)372  2)196  8)472  7)588  3)552 


9)468 

7)259 

6)888 

3)207 

6)390 

4)348 

Exercise  8. 

Addition 

1         6 

4 

7         3 

9 

4 

6 

3 

2         1 

2        2 

3 

5         7 

3 

2 

3 

2 

2        3 

6        3 

8 

5        4 

7 

8 

8 

6 

7         5 

2         4 

0 

7         9 

6 

4 

9 

8 

5         0 

7         9 

8 

8        3 

5 

8 

4 

2 

7         9 

6          9 

1 

4 

5 

9 

6 

7 

5          7 

6          1 

1 

2 

4 

6 

1 

6 

3          5 

6          6 

7 

8 

8 

0 

7 

6 

2          6 

1          1 

5 

7 

3 

6 

9 

2 

8          7 

5          9 

8 

9 

4 

5 

9 

7 

8          5 

Exercise  9. 

Subtraction 

43      39 

53      '. 

11      28 

67 

97      51      25      30 

75      60 

4       3 

9 

3        2 

8 

2 

9 

3       9 

9        6 

44 

16 

33 

52 

67 

45 

28 

42 

39 

20 

85 

35 

7 

4 

8 

5 

2 

6 

6 

4 

9 

2 

8 

2 

55 

31 

19 

36 

61 

45 

32 

30 

57 

38 

44 

54 

7 

6 

5 

8 

5 

5 

8 

8 

6 

7 

4 

6 

If  these  exercises  are  mimeographed,  the  order  of  the  examples  should 
be  frequently  changed  to  prevent  memorizing  the  answers. 


EXERCISES  FOR  SPEED  AND  ACCURACY         7 
Exercise  10.    Multiplication 


29 

46 

57 

27 

70 

27 

93 

42 

39 

5 

6 

4 

9 

6 

8 

4 

7 

5 

80 

72 

19 

89 

39 

96 

38 

68 

96 

6 

9 

7 

8 

6 

2 

4 

3 

9 

65 

57 

34 

70 

84 

79 

61 

56 

87 

7 

5 

8 

4 

9 

3 

6 

8 

7 

Exercise  11.    Division 


9)657  8)672  5)420  8)504  7)665  2)152 


3)960  8)576  4)248  7)434  9)864  5)160 


6)192  5)450  9)963  4)200  8)560  4)164 

Exercise  12.    Addition 


9 

4 

3 

4 

2 

2 

9 

4 

6 

8 

2 

9 

4 

3 

3 

2 

1 

9 

9 

8 

2 

7 

1 

3 

8 

5 

6 

1 

5 

2 

4 

9 

6 

7 

4 

0 

3 

9 

7 

3 

7 

8 

8 

3 

6 

9 

9 

8 

3 

1 

5 

9 

6 

9 

3 

7 

6 

4 

7 

2 

1 

3 

5 

6 

5 

8 

7 

8 

4 

6 

6 

6 

5 

9 

9 

4 

6 

5 

8 

5 

5 

6 

2 

7 

9 

6 

3 

7 

1 

7 

5 

7 

2 

7 

3 

3 

4 

6 

3 

5 

9 

3 

6 

3 

6 

SEVENTH  YEAR 
Exercise  13.    Subtraction 


97 

92 

98 

71 

92 

93 

87 

82 

45 

47 

47 

60 

23 

54 

20 

69 

53 

37 

94 

95 

84 

35 

61 

65 

94 

96 

63 

36 

30 

18 

19 

38 

14 

10 

27 

28 

90 

83 

74 

90 

35 

66 

71 

92 

42 

11 

24 

49 

50 

28 

19 

32 

80 

29 

Exercise  14.    Multiplication 


489 
6 

908 
8 

578 
5 

629 
3 

942 
7 

905 
4 

529 
9 

920 
2 

388 

7 

493 
5 

438 
3 

308 
9 

476  847  736  321  175 

9  4  8  6  7 


Exercise  15.    Division 


7)5621  3)2856  2)1042 

Exercise  16.    Division 


7)3157  4)3468  2)1888  6)5058 


9)9487  3)2625  5)4320  8)2592 


79)237  54)432  78)390  96)288  83)249 

74)518  29)174  68)204  92)828  49)343 

58)232  79)474  88)528  63)504  91U55 


EXERCISES  FOR  SPEED  AND  ACCURACY 
Exercise  17.    Addition 


42 

16 

28 

69 

82 

37 

33 

94 

72 

85 

89 

78 

97 

99 

94 

76 

86 

43 

72 

75 

53 

76 

65 

36 

93 

95 

36 

43 

52 

94 

73 

89 

62 

83 

57 

54 

72 

62 

58 

64 

78 

29 

34 

45 

85 

64 

82 

84 

87 

83 

56 

98 

49 

79 

73 

75 

85 

32 

24 

46 

57 

59 

42 

68 

43 

52 

91 

70 

11 

28 

62 

69 

66 

32 

33 

53 

71 

75 

91 

20 

Exercise  18.    Addition 


84 

36 

57 

29 

33 

65 

78 

41 

92 

43 

75 

47 

69 

33 

59 

85 

49 

84 

79 

88 

78 

83 

66 

36 

18 

99 

39 

24 

73 

64 

58 

43 

96 

47 

46 

98 

73 

77 

68 

75 

75 

42 

88 

89 

96 

78 

44 

76 

Exercise  19. 

Subtraction 

435 

347 

723 

811 

900 

989 

156 

268 

597 

364 

612 

679 

551  823  791  814  919  956 

280  479  196  147  310  406 


950 

379 

963 

756 

676 

169 

197 

594 

297 

697 

10 


SEVENTH  YEAR 


Exercise  20.    Multiplication 


2735 
7 

4981 
5 

9730 
8 

6573 
4 

5387 
9 

9468 
2 

7509 
3 

5389 
6 

5628 
8 

7366 
5 

9648 
7 

2489 
4 

1249 
9 

Exercise  21. 

Division 

90)4140 

30)2370 

60)5760 

40)3880 

50)3950 

80)5920 

70)4760 

20)1780 

60)5940 


40)3920  90)5130 

Exercise  22.    Division 


70)6720 


41)1435 


22)1584 


32)1472 


51)4233 
Exercise  23.    Addition 


21)1953 


31)2418 


6 

7 

2 

9 

5 

6 

7 

3 

7 

7 

6 

4 

6 

1 

9 

7 

9 

1 

1 

9 

6 

7 

6 

9 

8 

5 

8 

4 

3 

7 

8 

7 

3 

9 

9 

9 

5 

5 

7 

1 

2 

8 

9 

1 

4 

5 

4 

7 

3 

3 

2 

7 

9 

5 

7 

1 

6 

8 

7 

8 

8 

9 

3 

8 

3 

8 

4 

4 

6 

6 

8 

2 

2 

3 

6 

6 

3 

4 

5 

9 

8 

1 

3 

5 

9 

2 

8 

8 

EXERCISES  FOR  SPEED  AND  ACCURACY       11 
Exercise  24.    Addition 


72 

59 

66 

18 

33 

67 

15 

75 

36 

89 

96 

66 

53 

71 

67 

98 

87 

65 

71 

78 

40 

68 

96 

49 

63 

28 

74 

39 

47 

56 

22 

83 

98 

95 

64 

64 

17 

69 

97 

45 

Exercise  25. 

Subtraction 

8233 

9391 

6413 

5742 

9831 

7665 

2678 

6373 

2765 

3894 

2062 

1486 

9584 

9482 

9341 

8510 

8921 

7123 

2886 

7073 

3968 

3727 

6949 

4476 

Exercise  26. 

Multiplication 

2166 

7260 

4368 

8974 

8950 

6 

6 

3 

8 

7 

6084 

8394 

8796 

9386 

1604 

9 

6 

4 

3 

8 

7235 

4162 

4658 

8 

— 

7 

5 

Exercise  27 

62)i 

^  Division 

I 

71)1704 

}224 

92)2300 

61)6124 


82)3444 


91)7553 


12  SEVENTH  YEAR 

Exercise  28.    Practice  Problems* 

Not  only  does  one  need  to  know  how  to  work  examples 
rapidly  in  addition,  subtraction,  multiplication,  and  division, 
but  he  also  needs  to  know  how  to  apply  these  processes  rapidly 
and  accurately  in  solving  problems. 

In  completely  solving  any  concrete  problem  the  following 
steps  are  used : 

(1)  Reading  and  interpreting  the  problem. 

(2)  Selecting  the  principles  and  processes  needed  in  its 
solution. 

(3)  Performing  the  computations. 

(4)  Checking  the  results. 

Be  sure  that  you  understand  what  is  asked  for  and  what  facts 
are  given  which  can  be  used  in  the  solution  of  the  problem.  In 
selecting  the  principles  or  processes  needed  to  solve  the  prob- 
lem, it  will  help  if  you  picture  the  problem  as  a  real  problem  and 
ask  yourself  what  processes  you  would  use  in  a  similar  real  situ- 
ation. In  checking  the  results,  ask  yourself  whether  the  answer 
is  reasonable,  viewed  from  the  conditions  of  the  problem,  as  well 
as  check  the  abstract  computations. 

In  the  following  exercise  merely  indicate  the  processes  used 
in  solving  each  problem: 

1.  A  real  estate  dealer  owns  a  farm  of  142  acres  worth 
$125  an  acre;  5  city  lots  worth  $1500  each,  and  a  store  valued 
at  $8750.     Find  the  value  of  all  of  his  property. 

iThis  list  of  problems  is  designed  for  drill  in  reasoning  out  the  solutions 
of  problems.  The  class  period  should  be  used  in  merely  indicating  the 
solutions  of  these  problems.  The  pupils  should  be  required  to  copy  the 
iadicated  solutions,  and  then  perform  the  computations  and  check  the 
results  for  seat  work  or  home  work.  This  tjT^e  of  lesson  gives  the  teacher 
an  excellent  opportunity  to  teach  a  pupU  how  to  attack  and  solve  a  con- 
crete problem. 


PRACTICE  PROBLEMS  13 

Indicating  the  solution:^  (142 X $125)  + (5 X $1500) +$8750  = 
value  of  all  of  his  property. 

2.  A  farmer  sold  5  jars  of  butter  containing  respectively 
24  lb.,  26  lb.,  29  lb.,  28  lb.,  and  31  lb.  Find  the  total  num- 
ber of  pounds  that  he  sold. 

Indicating  the  solution:  24+26+29+28+31  =  no.  of  lb.  sold. 

3.  A  boy  bought  a  pony  for  $55.  His  expenses  for  the  month 
amounted  to  $6.  He  sold  the  pony  for  $58.  Did  he  gain  or 
lose  and  how  much?     '^ 

4.  The  cost  of  drilling  a  well  was  40  ?5  per  foot  for  drilling 
and  80  j^  per  foot  for  the  iron  tubing.  If  the  well  was  drilled 
150  ft.  and  100  ft.  of  tubing  was  used,  how  much  did  it  cost? 

6.  The  distance  from  Chicago  to  St.  Louis  is  282  miles. 
What  will  a  round-trip  ticket  cost  at  3(4  per  mile? 

6.  A  man  bought  a  lot  for  $1250.  He  built  a  house  on  it 
that  cost  $5275  and  then  sold  the  property  for  $7000.  How 
much  did  he  gain? 

7.  In  1917,  the  House  of  Representatives  had  a  membership 
of  435.  If  the  population  of  the  United  States  was  approxi- 
mately 100,000,000  at  that  time,  what  was  the  number  of  people 
to  one  representative? 

8.  A  farmer  exchanges  36  bushels  of  apples  at  $1  per  bushel 
for  coal  at  $8  per  ton.    How  many  tons  does  he  receive?    ^ 

9.  Mr.  Brown  bought  a  house  for  $8000.  He  paid  $2006 
down  and  agreed  to  pay  the  balance  in  8  equal  yearly  payments. 
How  large  was  each  payment? 

10.  A  real  estate  man  trades  40  front  feet  of  city  ground  at 
$240  a  front  foot  for  a  Western  farm  of  80  acres.  How  much 
is  the  farm  worth  per  acr^? 

1  Parentheses  should  be  used  to  separate  the  various  steps  in  the  problem 
in  order  to  el'minate  the  necessity  lor  teaching  the  law  of  signs. 


14  SEVENTH  YEAR 

11.  If,  as  computed,  the  water  area  of  the  earth  is  approxi- 
mately 144,500,000  square  miles  and  the  total  surface  of  the 
earth  is  approximately  196,907,000  square  miles,  how  much 
more  water  surface  than  land  is  there? 

12.  If  the  flow  of  water  through  the  Chicago  Drainage 
Canal  is  360,000  cubic  feet  per  minute,  how  much  water  passes 
through  it  in  24  hours? 

13.  A  building  worth  $400,000  was  damaged  to  the  amount 
of  $75,000  by  fire.  The  owners  received  from  an  insurance 
company  $60,000  damages.  What  was  the  net  loss  to  the 
owners  of  the  building? 

14.  A  falling  body  drops  144  feet  in  three  seconds  and  256 
feet  in  four  seconds.    How  far  does  it  drop  in  the  fourth  second? 

15.  The  product  of  four  numbers  is  10,920;  three  of  the  num- 
bers are  7,  8  and  15.    What  is  the  fourth  number? 

16.  A  gallon  contains  231  cubic  inches.  How  many  gallons 
are  there  in  a  cubic  foot  (1728  cubic  in.)? 

17.  A  man  had  $1275.45  on  deposit  in  a  bank.  He  gave 
checks  for  the  following  amounts:  $110.00;  $25.00;  $222.50; 
$8.75  and  $76.25.  What  was  his  balance  in  the  bank  after 
those  checks  had  been  cashed? 

18.  15  acres  of  potatoes  yielded  4125  bushels.  What  was 
the  average  yield  per  acre? 

19.  Mr.  Jones  bought  70  acres  of  land  for  $5530.  How  much 
did  he  pay  per  acre? 

20.  A  speculator  bought  wheat  in  the  fall  of  1916  for  $1.59 
per  bushel  and  sold  it  for  $1.73  per  bushel.  How  much  did  he 
make  if  he  handled  500,000  bushels  in  the  deal? 

21.  A  man  earns  $1200  a  year.  His  expenses  per  year  are 
$975.  In  how  many  years  can  he  save  $1800  under  those 
conditions? 


PRACTICAL  PROBLEMS  15 

22.  Mrs.  Klein  bought  2  dozen  eggs  at  38  cents  per  dozen, 
2  pounds  of  butter  at  57  cents  per  pound  and  10  pounds  of 
sugar  for  f  LIO.  How  much  change  should  she  receive  from 
a  ten-dollar  bill? 

23.  A  grocer  bought  300  sacks  of  flour  at  $1.25  per  sack  and 
paid  $12.00  freight  on  the  whole  amount.  He  is  selling  the 
flour  at  $1.50  per  sack.  How  much  profit  does  he  make  on 
each  sack? 

24.  A  man  bought  three  houses.  He  paid  $5500  for  the 
first;  $4565  for  the  second  and  $7750  for  the  third.  He  sold 
the  three  houses  for  $18,500.    How  much  did  he  gain? 

25.  A  farmer  sold  1600  bushels  of  rutabagas  at  35^  per  100 
pounds  (1  bu.  of  rutabagas  weighs  52  lb.).  How  much  did  he 
receive  for  them? 

26.  A  dealer  bought  3726  bushels  of  wheat  at  $2.03  per 
bushel  and  sold  it  at  $2.07  per  bushel.  How  much  did  he  make 
on  the  transaction? 

27.  A  grocer  bought  a  box  containing  100  apples  for  $2.00. 
Ten  of  them  spoiled.  He  sold  the  remainder  at  5  cents  each. 
How  much  did  he  gain  on  the  box  of  apples? 

28.  John  has  45  marbles.  Harry  and  James  each  have 
9  times  as  many  as  John.    How  many  marbles  do  they  all  have? 

29.  If  the  daily  pay  of  a  railroad  conductor  is  $4.80  for 
an  8-hour  day,  what  is  his  salary  for  a  year  of  330  working  days 
if  his  overtime  amounts  to  320  hours  and  is  paid  at  one 
and  a  half  times  the  regular  rate? 

30.  A  man's  estate  amounted  to  $15,630.  His  wife  received 
$6000  and  the  rest  was  divided  equally  among  his  three  children. 
How  much  did  each  receive? 

31.  11,161,000  bales  (500  pounds  each)  of  cotton  were  raised 
in  the  U.  S.  in  1916.    Find  the  production  in  pounds. 


16  SEVENTH  YEAR 

32.  A  dairyman  has  several  cows  in  his  herd  which  are  un- 
profitable. How  much  will  he  receive  if  he  sells  six  of  them 
weighing  1205,  1115,  1155,  1075,  1130,  and  1145  pounds  at 
$11.50  per  cwt.? 

33.  The  expenses  for  food  in  a  student's  boarding  club  of  38 
members  amounted  to  $110.84  for  one  week.  What  was  the 
total  cost  per  student  if  each  pays  75  cents  extra  to  cover 
hired  help  and  other  incidental  expenses? 

34.  Mr.  Warner  has  $8450  in  cash  with  which  he  wishes  to 
buy  a  farm.  He  reads  an  advertisement  of  a  farm  of  120  acres 
for  sale  at  $175  an  acre.  The  terms  are  j  cash  and  the  balance 
on  time.  If  he  buys  the  farm  and  pays  j  cash,  how  much  will 
he  have  left  to  buy  stock  and  farm  implements? 

35.  Andrew  bought  18  young  hens  for  $27.00.  He  spent 
$5.75  in  repairing  the  poultry  house  on  their  lot.  His  total  bill 
for  feed  was  $35.65.  His  receipts  for  eggs  were:  October 
$3.16,  November  $5.15,  December  $8.04,  January  $10.78,  Feb- 
ruary $12.84,  March  $9.23,  April  $8.91,  May  $7.96,  June  $6.50, 
July  $5.94,  August  $5.39,  and  September  $4.98.  His  hens  were 
worth  $1.25  each  at  the  end  of  the  year.  Find  his  net  profit  for 
the  yea-. 

36.  Ellen  pieced  a  quilt  for  her  mother.  The  pattern  which 
she  selected  makes  a  block  8  inches  square.  She  made  the  quilt 
2  yards  wide,  using  5  blocks  and  filling  in  the  places  between 
the  blocks  with  plain  strips.  How  wide  was  each  of  the  4  plain 
strips?  If  she  used  6  blocks  in  making  the  length  and  filled  in 
with  5  plain  blocks  of  the  same  size,  how  long  was  the  quilt? 

87.  An  agent  bought  1000  bushels  of  corn  at  $1.18  a  bushel 
and  sold  it  at  $1.27  a  bushel.     Find  his  gain. 

38.  A  carpenter  worked  2  days  (10  hours  each)  and  6  hours. 
What  did  he  receive  at  65  cents  an  hour? 


PRACTICE  PROBLEMS  17 

39.  Dorothy's  mother  asked  her  to  figure  up  the  milk  bill  for 
the  month  of  January.  They  used  2  quarts  per  day  and  5 
extra  quarts  during  the  month.  The  milk  cost  14  cents  a 
quart.    What  was  the  amount  of  the  bill? 

40.  A  farmer  had  16  ducks  to  sell.  On  November  1  they 
averaged  5^  pounds  each  and  he  was  offered  31  cents  a  pound. 
On  November  25  they  averaged  6  pounds  and  he  sold  them  for 
34  cents  a  pound.  What  was  his  additional  profit  in  the  24 
days  if  the  extra  feed  cost  $2.38? 

41.  Fred  raised  44  bushels  of  popcorn.  He  sold  9  bushels  to 
a  grocer  and  kept  1  bushel  for  his  own  use.  He  shelled  the 
remainder  and  shipped  it  to  the  city,  receiving  9  cents  a  pound. 
A  bushel  of  shelled  corn  weighs  56  pounds.  How  much  did  he 
receive  for  the  corn  which  he  shipped  to  the  city? 

42.  Ethel  worked  in  a  candy  factory  8  hours  per  day  and  1 
hour  overtime  each  of  24  days.  She  received  30  cents  an  hour 
for  regular  time  and  one  and  a  half  the  regular  rate  for  over- 
time.    How  much  did  she  earn  in  the  24  days? 

43.  The  girls  in  a  high-school  graduating  class  made  a  rule 
that  their  graduating  outfits  were  not  to  cost  more  than  $20.00. 
Martha  bought  5  yards  of  material  at  $1.25  a  yard;  3  yards  of 
lace  at  30  cents  a  yard;  48  inches  of  ribbon  at  30  cents  a  yard; 
hooks  and  eyes  10  cents;  thread  10  cents.  She  bought  a  pair  of 
silk  stockings  for  $2.00  and  a  pair  of  shppers  for  $6.50.  The 
dressmaker  charged  her  $4.00.  How  much  less  than  the  allow- 
ance did  her  outfit  cost? 

44.  Given  the  weight  of  a  load  of  wheat,  the  number  of 
pounds  in  a  bushel  of  wheat,  and  the  price  per  bushel,  how 
do  you  find  what  will  be  received  for  the  load  of  wheat? 

46.  Given  the  weight  of  a  jar  full  of  butter,  the  weight  of  the 
jar,  and  the  price  per  pound,  how  do  you  find  the  value  of  the 
butter? 


18 


SEVENTH  YEAR 


Exercise  29.  Addition 

89 

57 

75 

22 

28 

68 

35 

85 

72 

79 

94 

37 

87 

68 

55 

88 

86 

18 

36 

48 

24 

66 

10 

13 

79 

63 

93 

29 

59 

94 

97 

36 

43 

65 

93 

65 

42 

47 

36 

68 

Exercise  30.    Subtraction 


66240 

51212 

57510 

57230 

84792 

18017 

21538 

15691 

16583 
95831 

14916 

85096 

94030 

94265 

53526 

74830 

92508 

36279 

43630 

18037 

Exercise  31.  Mtiltiplication 

36 

67 

18 

92 

74 

63 

59 

80 

40 

20 

50 

90 

70 

60 

21 

74 

58 

30 

21 

69 

78 

80 

60 

90 

40 

70 

30 

50 

96 

48 

96 

75 

74 

34 

89 

70 

40 

90 

80 

70 

90 

80 

Exercise  32.    Division 


29)2014 


48)1392 


79)6557 


EXERCISES  FOR  SPEED  AND  ACCURACY       19 
Exercise  33.    Addition 


7 

2 

4 

8 

4 

3 

6 

9 

9 

4 

5 

6 

8 

7 

2 

8 

6 

7 

4 

4 

3 

2 

8 

9 

7 

5 

6 

5 

9 

2 

8 

7 

3 

9 

2 

3 

6 

9 

9 

6 

2 

6 

4 

1 

1 

8 

9 

9 

9 

6 

6 

8 

3 

1 

7 

2 

7 

8 

4 

1 

7 

7 

6 

6 

6 

9 

3 

6 

8 

1 

8 

9 

1 

2 

7 

8 

9 

6 

3 

7 

Exercise  34.    Addition 


24 

97 

92 

79 

18 

17 

99 

68 

73 

54 

64 

61 

79 

37 

76 

65 

95 

55 

39 

78 

87 

99 

92 

56 

96 

42 

88 

79 

83 

72 

92 

61 

63 

87 

26 

61 

56 

96 

24 

38 

Exercise  35.    Multiolication 

46        93        39        27        71        90        41        60        68        58 
38        72        96        57        29        70        86        13        78        42 


Exercise  36.    Division 
38)2014  99)4653  89)5162 


20 

SEVENTH  YEAR 

Exercise  37.    Addition 

355 

647                   258                   124 

677 

384                   186                   646 

894 

908                   257                   157 

901 

199                   649                   891 

786 

786                    558                    779 

Exercise  38.    Subtraction 

93344 

73561               61345              9238G 

61459 

27887              46950              58605 

82236 
56959 


62486 
24986 


98489 
78092 


91518 
24729 


Exercise  39.    Multiplication 


93 

62 

53 

75 

64 

94 

75 

40 

59 

70 

66 

91 

85 

73 

95 

83 

40 

62 

51 

84 

Exercise  40.     Division 


72)6552 


58)5278 


42)3402 


69)1104 


62)4650 

71)3763 
Exercise  41.    Multiplication 

92)2492 

76        86 

21        61        92        80        58        14 

74        91 

94        82 

13        60        26        35        69        54 

91        37 

Exercise  42.    Division 

EXERCISES  FOR  SPEED  AND  ACCURACY       21 


Exercise  43.    Addition 


7 

3 

4 

2 

7 

3 

8 

9 

7 

5 

3 

7 

5 

6 

3 

9 

2 

6 

3 

2 

5 

2 

4 

8 

6 

1 

6 

2 

8 

9 

8 

6 

6 

6 

9 

9 

9 

6 

4 

3 

7 

3 

9 

4 

8 

5 

4 

4 

7 

6 

4 

8 

6 

4 

5 

8 

1 

3 

5 

9 

9 

7 

5 

7 

6 

3 

9 

6 

6 

1 

3 

9 

8 

1 

7 

7 

7 

9 

6 

3 

Exercise  44.    Subtraction 


812130 
315387 

762325 
164729 


826364 
117789 

953276 
154397 


951349 
386360 

823427 
385798' 


943147 
684059 

934399 
169936 


Exercise  45.    Multiplication 


461 
38 


380 
59 


257 
62 


502 
17 


418 
64 


936 
49 


Exercise  46.    Division 


8)7688 


5)3755 


9)7758 


6)5802 


2)1578 


4)3740 


7)6832 


8)6800 


22 


SEVENTH  YEAR 
Exercise  47.    Addition 


6467 

8759 

2866 

4934 

6976 

8988 

2678 

7087 

9893 

3597 

9668 

6233 

4066 

9815 

6086 

6963 

6417 

4934 

2849 

9713 

Exercise  48.    Multiplication 

795 

317 

714 

873 

391 

809 

86 

27 

45 
Exercise  49. 

36 
Division 

91 

39 

4)39320 

6)15432 

9)71505 

2)17590 

7)62594 

3)29049 

8)29960 

6)49315 

Exercise  50. 

Division 

49)3136 

88)1672 

69)4425 

Exercise  51. 

.  Addition 

6989 

3976 

8698 

4356 

7519 

5787 

4699 

5367 

8878 

7195 

8749 

3999 

7964 

1654 

2425 

9587 

3580 

1789 

9283 

7786 

Exercise  52.    Multiplication 

629 

386 

542 

578 

468 

851 

67 

89 

47 

19 

52 

87 

EXERCISES  FOR  SPEED  AND  ACCURACY       23 


EXERCISE  63.    Addition 


3 

7 

2 

4 

5 

8 

9 

4 

7 

3 

9 

6 

5 

8 

6 

4 

3 

3 

3 

8 

3 

9 

8 

2 

6 

7 

7 

3 

0 

7 

6 

1 

1 

7 

9 

4 

6 

9 

9 

7 

5 

5 

8 

7 

4 

6 

6 

6 

5 

7 

8 

1 

4 

9 

7 

3 

9 

2 

6 

2 

8 

6 

9 

8 

1 

2 

9 

4 

7 

5 

2 

8 

4 

8 

8 

1 

2 

9 

1 

7 

8 

6 

9 

2 

Exercise  54.    Multiplication 


6629 
964 

7216 
378 

Exercise  66.    Division 

9460 
325 

8)778896 

6)394820 

9)849384 

6)621844 

4)316744 
Exercise  66.    Division 

7)689199 

68)1768 

39)3649 
Exercise  67.    Division 

78)4446 

98)6978 


83)4897 


67)6628 


24 


SEVENTH  YEAR 


Exercise  68.    Addition 


783 

816 

238 

696 

739 

893 

684 

464 

681 

369 

377 

769 

575 

471 

579 

736 

237 

548 

828 

284 

756 

864 

599 

169 

623 

798 

Exercise  59.    Multiplication 

773 

5629 

7216 

9450 

964 

378 

Exercise  60.    Division 

325 

94)7426 

75)3675 
Exercise  61.    Multiplication 

46)3956 

4509 

9486 

2768 

847 

607 

Exercise  62.    Division 

745 

3)21642 

7)42091                 6)36318 

8)55848 

5)35215 


9)61488  4)28260 

Exercise  63.    Division 


6)54084 


84)5712 


63)3591 


87)6003 


EXERCISES  FOR  SPEED  AND  ACCURACY       25 


6745 
7565 
6070 
8775 
6984 
6190 
6870 
9820 


8397 
378 


85)49895 


7652 
994 


Exercise  64.  Addition 

3667 
8643 
5080 
9150 
5921 
9382 
9832 
1390 


Exercise  65.    Multiplication 

3014 
947 


Exercise  66.    Division 


Exercise  67.    Multiplication 

7381 
629 


7354 
5454 
9270 
7280 
8777 
9290 
8680 
8979 


5713 
528 


97)81092 


8439 
852 


Exercise  68.    Division 


93)69657 


83740 
7483 


Exercise  69.    Multiplication 


76)63536 


29561 
495 


26 


SEVENTH  YEAR 


Exercise  70 

Most  stores  now  have  cashiers 
to  make  change  for  their  customers. 
This  is  much  more  economical  be- 
cause the  cashier  by  constant  prac- 
tice becomes  much  more  efficient 
than  would  be  possible  for  the  many 
clerks  whose  attention  is  mainly 
devoted  to  selling  goods. 

The  modern  method  of  making  change  for  a  purchase  is  by 
addition.  For  example,  if  you  sell  goods  to  thb  amount  of  SI. 73 
and  receive  a  five-dollar  bill  from  the  purchaser,  instead  of 
subtracting  $1.73  from  $5.00  you  start  with  the  amount  $1.73 
and  take  2^,  25^  and  3  one-dollar  bills  from  the  change  drawer 
and  say  to  the  purchaser  $1.73,  $1.75,  $2.00,  $3.00,  $4.00, 
$5.00.  This  method  is  not  only  quicker,  but  saves  the  purchaser 
the  trouble  of  counting  his  change.  Practice  making  change 
in  this  way  for  the  following  purchases. 


Amount  of  purchase 

1.  $  0.12 

2.  $  3.48 

3.  $  1.06 

4.  $  5.28 

5.  $     .08 

6.  $11.27 

7.  $12.39 

8.  $  7.33 

9.  $     .65 

10.  $  2.48 

11.  $    .42 

12.  $     .73 

13.  $  1.62 


Amount  of  money 
presented  to  the  cashier 

A  dollar  bill 

Ten-dollar  bill 

Two  dollar  bills 

Two  five-dollar  bills 

A  dollar  bill 

A  ten-  and  a  five-dollar  bill 

Three  five-dollar  bills 

Ten-dollar  bill 

Five-dollar  bill 

Three  dollar  bills 

A  half-dollar 

A  dollar  bill 

A  two-dollar  bill 


CHAPTER  II 
REVIEW  OF  COMMON  FRACTIONS 

Exercise  1.    Three  Meanings  of  a  Fraction 

The  fraction  f  may  have  any  one  of  three  meanings.  (1)  It 
may  mean  3  of  the  4  equal  parts  of  a  thing;  (2)  j  of  3  equal 
things;  or  (3)  3  divided  by  4. 

For  example:  an  inch  is  divided  into  fourths,  f  of  an  inch 
may  mean  3  of  the  4  equal  parts  of  an  inch;  f  of  3  inches; 
or  the  quotient  of  3  inches  divided  by  4. 

■^ 1 3  of  the  4  equal  parts  of  an  inch.  ' 


\                          I  ^  of  3  inches. 
1 13  inches -r- 4. 


The  above  diagram  shows  the  three  meanings  of  the  fraction 
f .    Work  these  three  meanings  out  on  your  ruler. 

Exercise  2.    Reduction  to  Lowest  Terms 

The  denominator  4  of  the  fraction  indicates  the  size  of  the 
equal  parts  by  showing  into  how  many  equal  parts  the  whole 
has  been  divided.  The  numerator  3  shows  the  number  of  these 
equal  parts  which  form  the  fraction. 

1.  Show  the  three  meanings  that  the  fraction  -^  may  have. 

2.  In  the  fraction  ^  what  is  the  denominator?     What  is 
the  numerator? 

3.  This  fraction  shows  that  the  whole  has  been  divided 
into  how  many  equal  parts? 

4.  How  many  of  these  parts  have  been  taken  to  form  the 
fraction? 

27 


28  SEVENTH  YEAR 

6.  Answer  the  same  questions  for  the  foUovsdng  fractions: 

9       6.    A    2      7.     15 
T^}   8»   6>   3»    8»    16" 


6.  Divide  both  the  numerator  and  the  denominator  of  the 
fraction  -^  by  4.    What  is  the  result? 

7.  Compare  the  fraction  f  with  the  fraction  ^,  using 
the  above  diagram.  Show  that  the  two  fractions  are  equal 
by  using  your  ruler. 

8.  Divide  both  terms  of  the  fraction  ^  by  3.  Use  your 
ruler  to  compare  the  result  with  j^. 

9.  Divide  both  terms  of  the  fraction  |  by  2.  Compare  the 
result  with  ^. 

10.  Multiply  both  terms  of  the  fraction  f  by  3.  Use  your 
ruler  to  compare  the  result  with  f . 

11.  Multiply  both  terms  of  the  fraction  |^  by  2.  Compare 
the  result  with  ^. 

Use  other  examples,  if  necessary,  to  make  clear  the  following: 

PRINCIPLE:  When  the  numerator  and  denominator  of  a  frac- 
tion are  both  multiplied  by  or  both  divided  by  the  same 
niunber,  the  value  of  the  fraction  is  not  changed. 

When  the  numerator  and  denominator  of  a  fraction  are 
both  divided  by  the  same  number,  the  fraction  is  said  to  be 
reduced  to  lower  terms. 

When  both  terms  are  multiplied  by  the  same  number,  the 
fraction  is  said  to  be  reduced  to  higher  terms. 


t 

7. 

12 
20 

13. 

15 
25 

19. 

60 
90 

25. 

35 
49 

9 
12 

8. 

1  5 
20 

14. 

32 

48 

20. 

14 

28 

26. 

28 
3  5 

1 

9. 

15 
2  1 

15. 

1  8 
24 

21. 

1  6 
32 

27. 

42 
48 

9 
15 

10. 

20 
30 

16. 

30 
36 

22. 

32 
36 

28. 

72 
81 

12 
16 

11. 

14 
16 

17. 

15 

27 

23. 

33 

44 

29. 

100 
125 

16 

18 

12. 

16 
2T 

18. 

32 

42 

24. 

2  1 

28 

30. 

125 
200 

REVIEW  OF  FRACTIONS  29 

12.  Change  ^  to  higher  terms  by  multiplying  both  terms  by  2 ; 
by  3;  by  5.  Reduction  to  higher  terms  is  used  in  reducing 
fractions  to  a  common  denominator. 

13.  Which  is  shorter:  To  divide  both  terms  of  ^  by  5,  and 
then  both  terms  of  the  result  by  3,  or  to  reduce  to  lowest  terms 
by  dividing  both  terms  of  ^  by  15? 

Reduce  to  lowest  terms: 
1. 
2. 
3. 
4. 
6. 
6. 

Exercise  3.    Addition  and  Subtraction  of  Similar  Fractions 
Similar  fractions  are  fractions  having  the  same  denominator. 

1.  $3 +$4  are  how  many  dollars? 

2.  3  books+4  books  are  how  many  books? 

3.  3  fourths+4  fourths  are  how  many  fourths? 

A.      3_1_4_? 

4.  4+4-4- 

The  form  f +x  means  the  same  as  3  fourths+4  fourths. 
Which  is  more  quickly  written?  Which  form  occupies  the 
least  space? 

If  we  use  the  more  convenient  form  f  for  3  fourths,  we  must 
not  forget  that  the  denominator  merely  indicates  the  name 
or  size  of  the  equal  parts.  The  numerator  shows  how  many  of 
these  equal  parts  compose  the  fraction.  In  adding  the  frac- 
tions f +1^,  we  are  merely  adding  two  numbers  of  fourths, 
making  ^.  How  shall  we  proceed,  then,  in  subtraction  of 
similar  fractions? 


t 

+ 

i 

= 

f 

+ 

2 

T 

= 

A 

— 

3 

rr 

= 

1 

4 

+ 

2 

4 

= 

3 
5 

+ 

1 
5 

= 

7 
8 

— 

f 

= 

f 

— 

f 

= 

8. 

5.  _|_    2.  _ 
717 

9. 

11         6    _ 
13       13- 

10. 

f-f  = 

11. 

f  +  f  = 

12. 

1     1      2    _ 
3  T^   3    "~ 

13. 

4  3    _ 

5  ~    5    — 

lA 

9   J-  A  = 

15. 

2     1      5           3 
7   -T    7           7 

16. 

5     1      4    ..      2 
1  1    1    1  1        11 

17. 

5           2     1      7 
"9    -    9"  -T  -9 

18. 

3      1      2            1 
5   "t"    5    ~    5 

19. 

7  2           3 

8  ~    8"  ~    8 

20. 

1  1    1      9           3 
13    1    13        13 

21. 

3     1      2     1      4 
5+5  +   5 

30  SEVENTH  YEAR 

Add  or  subtract  the  following: 
1. 
2. 
3. 
4. 
6. 
6. 
7. 

Exercise  4.    Addition  and  Subtraction  of  Dissimilar  Fractions 

Dissimilar  fractions  are  fractions  not  having  the  same  denom- 
inators. 

Can  you  add  $3  and  4  books  together?  You  can  not  unless 
you  say  3  things  and  4  things  are  7  things;  or  3  articles +4 
articles  are  7  articles.  Only  like  numbers  can  be  added  or 
subtracted.  The  term  thing  or  article  might  be  called  the 
common  denominator  of  the  two  numbers. 

Can  we  add  f +4?  What  must  be  done  before  we  can  add 
them?  What  is  the  least  common  denominator  of  these  two 
fractions? 

The  following  form  will  be  found  very  convenient  for  adding 
dissimilar  fractions: 


I  I  1  _°~Lr_ij7  _  i_5_ 

t~r4 775 12  "•'^12 


The  advantages  of  writing  the  denominator  once  as  in  the 
form  above  are  (1)  it  is  shorter;  (2)  it  indicates  the  common 
denominator  more  clearly  and  (3)  shows  that  only  the  numer- 
ators are  to  be  added.     The  expression  -^^  should  be  read 


12  T^   12" 


REVIEW  OF  FRACTIONS 


31 


Add  or  subtract  as  indicated : 
1. 
2. 
3. 
4. 
6. 
6. 

After  the  pupils  understand  these  problems,  put  the  work  on  a  time 
basis  and  give  a  drill  exercise.  8  minutes  is  suggested  as  a  suitable  time 
limit  for  the  average  class. 


2      I      1    _ 
315    — 

7. 

5  1      5    _ 

6  -1-2  1- 

13. 

5     1      3    _ 
12+   8    - 

19. 

8  2    _ 

9  —    3   - 

11  3    _ 

12  8    — 

8. 

1   _    3    _ 
8           5    — 

14. 

2   4.    5.  _ 
5   +    9    — 

20. 

7  ,      3    _ 

8  T^    4    — 

V     1      3    _ 
8   T^    5    — 

9. 

7     1      2    _ 
15+    6    - 

16. 

3  3 

4  ~"    8    — 

21. 

5.  _    2.   _ 
9           4    — 

13  3    _ 

14  4    - 

10. 

3  5    _ 

4  18- 

16. 

5           1    _ 
7    ~    3    — 

22. 

3  1      5    _ 

4  T^IB  — 

1  li      5    _ 
21+    7    - 

11. 

1            3    _ 

4         14  — 

17. 

1  4.    2    _ 

2  i^   3    — 

23. 

11          5    _ 
14          7    - 

5  8    _ 

6  14  — 

12. 

7  3    _ 

8  4    — 

18. 

3      1      2 
8   +    5    — 

24. 

15          7    _ 
18    -12- 

Exercise  5.    Addition  and  Subtraction  of  Mixed  Numbers 

In  addition  and  subtraction  of  mixed  numbers  the  form 
shown  below  is  one  of  the  most  convenient : 
Example:     Add  3f ,  12},  7j,  ISj. 

As  shown  in  the  illustration,  the  least  common 
denominator  is  found  and  written  below  the 
line.  The  numerators  are  then  placed  to  the 
right  of  the  vertical  line,  the  sum  being  -f-j- 
or  If^.    This  sum  is  then  added  to  the  integers, 


3f 

9 

i2i 

18 

'3 

8 

i5i 

12 

38M 

47 

24 

making  3S^. 


Add: 
1.  13j 

8f 
27t 
43f 


2. 


25j 

8i 
38f 


3. 


48i 
62j 
95J 
86f 


4. 


5. 


7| 
6| 


2lf 

36t 

48| 

91 


Subtract: 

6.  9j-5| 

7.  25i-8| 


8.  16^-  9* 


10.  7|— 4t 

11.  12   -8| 


32  SEVENTH  YEAR 

12.  A  box  of  scouring  brick  weighed  60f  lb.  The  box  itself 
weighed  4^  lb.    How  much  did  the  scouring  brick  weigh  ? 

13.  The  sum  of  two  numbers  is  28^.  One  of  the  numbers  is 
17f .    What  is  the  other? 

14.  In  two  bins  of  potatoes  there  are  128^  bu.  In  one 
there  are  62  j  bu.     How  many  are  there  in  the  other? 

15.  A  flagstaff  62^  ft.  high  was  made  of  two  poles  spliced 
together.  The  lower  pole  was  28 §  ft.  tall.  How  much  did 
the  upper  pole  add  to  its  height? 

16.  A  kite  string  286^^  ft.  long  broke  at  a  distance  of  127^ 
ft.  from  the  lower  end.  What  length  of  string  went  with  the  kite? 

17.  A  clerk  earned  $90  per  month.  His  expense  for  board, 
for  this  period,  was  $30^;  for  laundering,  $5^;  for  articles 
of  clothing,  $14  J ;  for  life  insurance,  $3j;  for  incidentals, 
$14  f.      What  was  the  surplus  for  the  month? 

18.  A  boy  sawed  a  piece  of  board  exactly  20  inches  long 
from  a  board  26 1-  inches  long.  Allowing  ^  of  an  inch  for  the 
cut  of  the  saw,  find  the  length  of  the  piece  that  was  left. 

19.  Four  boards  were  glued  together  for  a  table  top.  When 
planed  for  the  glue  joints,  they  measured  6f  in.,  7|-  in.,  7  j  in. 
and  6j^  in.  respectively.  Find  the  width  of  the  table  top. 
How  much  would  have  to  be  planed  off  this  top  to  make  it 
27  in.  in  width. 

20.  A  school  room  is  12  ft.  high.  The  picture  molding  is 
3f  ft.  from  the  ceiling.    How  far  is  the  molding  from  the  floor? 

21.  How  wide  must  a  strip  of  goods  be  cut  to  make  a  ruffle 
3  in.  wide  when  finished  if  ^  in.  is  turned  under  for  the  heading 
and  f  in.  is  used  for  the  lower  hem? 

22.  A  room  is  12  §^  ft.  long  and  11  f  ft.  wide.  How  many 
feet  of  base  board  are  required  to  go  around  the  room,  deducting 
3  J  ft.  for  the  door? 


REVIEW  OF  FRACTIONS  33 

Exercise  6.    Multiplication  of  Fractions 

3       2 
Example:  4  '^  S  ~  ^ 

Take  a  foot  ruler.  What  is  ^  of  a  foot  in  inches?  What  is  ^  of  ^  of 
a  foot  in  inches?  Show,  then,  that  ^  of  ^  of  a  foot=-^  of  a  foot.  4  of  f 
of  a  foot  =1^  of  a  foot?  -f  of  f  of  a  foot  =  1^  of  a  foot?  In  multipUcation 
of  fractions  the  word  oj  may  be  replaced  by  the  sign  X. 

Therefore:  fx|=T^. 

Compare  the  product  of  the  numerators  of  the  fractions  with  the  num- 
erator of  the  result,  3^. 

Compare  the  product  of  the  denominators  of  the  fractions  with  the 
denominator  of  the  result,  j^. 

Reduce  ^  to  its  lowest  terms. 

Cancellation  is  the  process  of  reducing  to  lower  terms  before  multiplying 
by  dividing  any  numerator  and  any  denominator  of  the  fractions  by  the 
same  number: 

1  1 

^^3"2 

2  1 

We  see,  then,  that  in  the  multipUcation  of  fractions  the  product  of 
the  numerators  of  the  fractions  becomes  the  numerator  of  the  result  and 
the  product  of  the  denominators  the  denominator  of  the  result,  cancellation 
being  used  to  shorten  the  process. 

Multiply  the  following  fractions :    Use  cancellation. 

^^'      8^5    Xt4  = 

WJL  V   ^   \/  1  8  
•      9   ^    3    -^24" 


1. 

8    >s/    3    _ 
I2X    9    - 

2. 

txf  = 

3. 

fXT^= 

4. 

I2X   3   - 

6. 

Ixi  = 

6. 

fxf  = 

7. 

1  V    5    _ 
3   -^    8    ~ 

8. 

4-^5   — 

9. 

9    V    2    _ 
llX    3    - 

10. 

le^TS"— 

11. 

5   -^32 

12. 

15y    9   — 
18'^12  — 

13. 

8   ''^    5   — 

14. 

Mxff= 

15. 

3  V   ^  — 

4  '^    3   ~ 

16. 

1   V   ^  - 

1  V   i  V    6- 

2  A    3   A    7 

5   V    2.  s/UL — 


19.    2X3^7" 


20.  tXfXt|  = 

01  21v36vl6_ 

^o.  28A24A    4   — 

**•  24Ai5AY^  — 


34  SEVENTH  YEAR 

25.  A  boy  glued  5  maple  strips  and  4  walnut  strips  together 
to  make  a  pen  tray.  If  each  of  the  strips  was  ^  in.  wide, 
how  wide  was  the  piece  for  the  tray? 

26.  A  teacher  asked  a  boy  to  make  him  a  book  case  for  a 
set  of  encyclopedias  consisting  of  30  volumes.  How  long  must 
the  boy  make  each  of  the  two  shelves  if  the  books  average 
2^  in.  in  thickness? 

27.  How  many  yards  of  ruffling  must  be  made  to  put  5 
ruffles  around  a  dress  skirt  three  yards  in  girth  if  §  extra  is 
allowed  for  the  gathering?  *• 

28.  How  much  will  f  of  a  yard  of  ribbon  cost  at  22  cents 
per  yard? 

29.  A  piece  of  goods  containing  6  quarter-inch  tucks  and  a 
1-in.  hem  is  20  in.  when  finished.  How  wide  was  it  before 
being  tucked  and  hemmed? 

30.  How  wide  must  a  piece  of  goods  be,  to  be  24  in.  wide 
when  complete,  if  we  allow  for  6  "one-eighth"  inch  tucks; 
6  "one-fourth"  inch  tucks  and  a  2-in.  hem? 

Exercise  7.    Division  of  Fractions 
In  division  of  fractions  we  may  use  two  methods:    (1)  reduce 
to  a  common  denominator  and  divide  the  numerators;  (2)  invert 
the  divisor  and  multiply. 

(1)  Example:    i-nf  =  |-|=it=f  or  li 

Note  that  you  are  dividing  12  fifteenths  by  10  fifteenths,  giving  as  a 
result  -j-g-  times — the  denominator  being  eliminated  in  the  division. 

, ^- (2)  Example:    |-5-f  =  ? 

1  Take  a  sheet  of  paper  and  fold  it 

into  thirds  as  in  the  illustration. 
'  How  many  times  will  the  shaded 

portion  representing  f  be  contained  in  the  whole  sheet? 


REVIEW  OF  FRACTIONS  35 

Since  a  whole  sheet  contains  f  of  a  sheet  1^  or  -f  times, 
f  of  a  sheet  contains  f  of  a  sheet  f  of  -f  times. 

2 

^Therefore:  4     2     4     3     6         1 

— ^-=-X-=-o^l- 
5     3     5     2     5        5 
1 

^  is  the  divisor.  We  see  that  the  %  has  been  inverted,  becoming  ^  when 
we  multiply.  By  using  the  above  method  with  other  examples  you  will 
find  that  the  divisor  is  always  inverted  before  you  multiply. 

PRINCIPLE:    To  divide  one  fraction  by  another,  invert  the 
divisor  and  multiply. 

This  method  is  preferred  to  reducing  to  a  common  denominator  because 
the  division  example  is  converted  into  a  multiphcation  example,  which 
is  the  easiest  of  all  the  processes  in  fractions. 


Divide  the  following  fractions: 
1. 


7 
8 
3 
5 
1 
2 
6. 
7 

_&_, 
12 


.     3 

—   4   — 

6. 

4  .     4    _ 

5  •    15- 

11. 

5     .      7    _ 
8     •    11  — 

le. 

3      .      1 

8    —    2 

.     9    _ 
•    11- 

7. 

36   .     4    _ 

48   •    16 

12. 

2  .      5 

3  —    6    — 

17. 

36    .    27 
40    •    35 

.     2    _ 
—    3    — 

8. 

2  ^  A  _ 

3  —    7    - 

13. 

«^f  = 

18. 

3^2 

4     •     9 

.     4    _ 
~    5    — 

9. 

7     .      1    _ 
¥  ~    3    - 

14. 

12    .      8    _ 
15   •    10- 

19. 

11.22 
12    •    30 

.     2 
-    3   — 

10. 

1  .      1    _ 

2  —    3   — 

15. 

9  -is- 

20. 

2  .      4 

3  —  ¥ 

Exercise  8.    Multiplication  and  Division  of  Mixed  Numbers 

How  do  you  change  a  mixed  number  to  an  improper  fraction? 
Which  is  easier:  to  divide  2f  by  if  or  to  divide  |-  by  ^?  In 
multiplication  and  division  of  mixed  numbers,  then,  it  is  easier 
first  to  reduce  the  mixed  numbers  to  improper  fractions  and 
then  perform  the  operation  of  multiplying  or  dividing. 

Multiply  or  divide: 

1.  3f  X2|   =  6. 

2.  eixif  =  6. 

3.  12f-^2f    =  7. 

4.  51h-3^    =  8. 


3iX8j 

= 

9. 

lfX2f  = 

2H3f 

= 

10. 

6iX6i  = 

2iXli 

= 

11. 

55"="32  = 

7i-^2i 

= 

12. 

q3^c1_ 
»5   •  '^3- 

36  SEVENTH  YEAR 

13.  4ix2|   =  17.  5fXli^=  21.  lfX3i  = 

14.  9jXlii=  18.  4|X3f  =  22.  8j-Mi  = 
16.  8f-^l|  =  19.  If-Mf  =  23.  2fX2|  = 
16.  Sj-f-lJ    =  20.  #■^3i    =  24.  2i-^3j  = 

25.  How  many  times  can  1  j  gallons  of  oil  be  drawn  from  a 
barrel  holding  31^  gallons? 

26.  How  many  bushels  of  apples  at  $lj  can  be  bought 
for  $7  J? 

27.  If  nine  hogsheads  hold  50f  bushels,  what  does  1  hogs- 
head hold? 

28.  How  many  pounds  of  bacon  at  $f  per  pound  can  be 
bought  for  $1^? 

29.  At  Slf  per  crate,  how  many  crates  of  peaches  can  be 
bought  for  $17  J? 

30.  A  railway  section  of  8^  miles  cost  for  construction 
$246,504  J.    What  did  it  cost  per  mile? 

31.  A  banker  bought  a  tract  of  timber  for  $7490,  at  $53^ 
per  acre.    How  many  acres  did  he  buy? 

32.  If  I  pay  $5f  for  books  at  $f  per  volume,  how  many 
volumes  do  I  buy? 

33.  At  $f  per  basket,  how  many  baskets  of  fruit  can  be 
bought  for  $27? 

34.  At  3§  miles  an  hour,  how  long  does  it  take  a  person 
to  walk  8  J  miles? 

36.  A  teacher  has  a  desk  book  rack  21  in.  long.  How  many 
text  books  averaging  ^  in.  thick  will  it  hold? 

36.  A  class  bought  two  strips  of  ribbon  of  different  colors 
for  class  colors.  They  divided  the  strips,  which  were  21^ 
yards  in  length,  into  32  equal  parts.    How  long  was  each  piece? 


REVIEW  OF  FRACTIONS  37 

37.  A  girl  making  a  base  for  a  letter  rack  wished  to  locate 
the  central  line.  If  the  base  board  is  3§  in.  wide,  how  far  will 
the  center  line  lie  from  each  edge? 

38.  When  sugar  is  selling  at  10^  cents  per  pound,  how  many 
pounds  are  sold  for  a  dollar  at  that  rate? 

Exercise  9.    Drill  on  the  Four  Processes  in  Fractions 


Solve  the  followi 

ng: 

1. 

3   w    3   _ 

4X9^- 

9. 

8     .    2_ 
"9—3- 

2. 

5  9  _ 

6  14- 

10. 

8    /^S  — 

3. 

1     1      3    _ 
8   +    4    — 

11. 

15  3_ 

16  4  — 

4. 

5    _^    2    _ 

12. 

3      r  i- 
8   +7  — 

6. 

9           3    _ 
12         8    - 

13. 

8    v^  — 
9^5  — 

6. 

ifxH= 

14. 

1     .    1_ 
3   ~2  — 

7. 

i-f  = 

15. 

4         2_ 
5—3  — 

8. 

3  I      3    _ 

4  "T    5    — 

16. 

1     i2_ 
3  +T- 

17. 

2    '^4 

18. 

i  4-i 
3   +4 

19. 

2  1 

3  "~4 

20. 

3  .    1 

4  ~  3 

21. 

3      12. 
5    +4 

22. 

3    ^^2 

23. 

7  .    3 

8  •   5 

24. 

30   .   5 
Sfi    •    ft 

25.  Find  the  cost  of  a  lOf-lb.  turkey  at  38  cents  a  pound. 

26.  How  much  will  a  4j-lb.  chicken  cost  at  24^  cents  a 
pound? 

27.  A  roast  weighing  4^  lb.  costs  99  cents.  How  much  was 
the  cost  per  pound? 

28.  A  barrel  of  flour  weighs  196  lb.  How  many  pounds  are 
there  in  a  j-bbl.  sack?    In  a  ^-bbl.  sack? 

29.  Obtain  local  prices  at  a  butcher  shop  and  find  the  cost 
of  2f  lb.  of  round  steak;  5^  lb.  of  rib  roast;  and  1§  lb.  of 
pork  chops. 

30.  A  man  owned  f  of  a  mill  and  sold  f  of  his  share.  What 
part  of  the  total  value  of  the  mill  did  he  sell?  What  part  of 
the  mill  did  he  still  own? 


348560 


88  SEVENTH  YEAR 

Exercise  10.    Review  of  Decimal  Fractions 

A  fraction,  whose  denominator  is  ten  or  some  product  of 
tens,  is  called  a  decimal.  The  value  of  a  figure  in  a  decimal 
is  shown  by  its  position  with  regard  to  the  decimal  point. 


EOT 
J2 


2  ^ 


1    1   1,1    1    1  .  1    1    1,1    1 


In  the  above  number  how  does  the  1  in  tenths  place  compare 
in  value  to  the  1  in  units  place?  How  does  the  1  in  units 
place  compare  in  value  to  the  1  in  hundreds  place?  How  does 
the  1  in  units  place  compare  in  value  with  the  1  in  tenths  place? 
How  does  the  1  in  units  place  compare  in  value  with  the  1 
in  thousandths  place?  Start  at  the  1  in  hundred  thousands 
place  and  go  to  the  right.  How  do  the  values  of  the  I's  change? 
Start  at  the  1  in  millionths  place  and  go  to  the  left.  How  do 
the  values  of  the  I's  change? 

The  number  above  is  read  one  hundred  eleven  thousand, 
one  hundred  eleven,  and  one  hundred  eleven  thousand  one 
hundred  eleven  millionths. 

Read  the  following  decimals: 


1. 

.001 

6. 

.375 

11. 

.7584 

16. 

.0875 

2. 

19.02 

7. 

3.1416 

12. 

.5236 

17. 

.00875 

3. 

.0005 

8. 

1.4142 

13. 

1.732 

18. 

.000875 

4. 

50.001 

9. 

2150.42 

14. 

8.75 

19. 

.005 

6. 

.00125 

10. 

.866 

15. 

.875 

20. 

.000005 

REVIEW  OF  DECIMALS  39 

How  many  decimal  places  are  needed  to  write  tenths; 
thousandths;  hundredths;  ten-thousandths;  millionths;  hun- 
dred-thousandths? Practice  on  this  question  until  you  can 
give  the  answers  instantly,  because  it  will  help  you  in  writing 
decimals. 

Write  in  figures :  ^ 

1.  One  hundredth.    -  ^' 

2.  Two  hundred  and  five  ten-thousandths. 

3.  Sixty-three  thousandths. 

4.  Twenty-five  hundredths. 

5.  Seven  hundred  fifteen  thousandths. 

6.  Eighty-seven  thousandths. 

7.  Nine  hundred  forty  thousandths. 

8.  Sixty-three  hundredths. 

9.  Sixty-seven  thousandths. 

10.  Eight  thousandths. 

11.  Five  ten-thousandths. 

12.  One  hundred  twenty-five  hundred-thousandths 

13.  Twenty-five  millionths. 

14.  Twenty-five  and  five  ten-thousandths. 

15.  One  hundred  and  forty-three  thousandths. 

16.  One  hundred  forty-three  thousandths. 

17.  Four  hundred  one  and  four  hundred  one  thousandths. 

18.  Three  and  twenty-five  ten-thousandths. 

19.  Eight  hundred  and  seven  millionths. 

^In  writing  decimals,  it  is  a  good  plan  to  have  no  erasers  at  the  black- 
board and  require  the  pupils  to  be  sure  of  the  number  of  places  before 
they  begin  writing  each  decimal  that  you  read  to  them. 


40  SEVENTH  YEAR 

Exercise  11.    Addition  and  Subtraction  of  Decimals 

Decimals  are  added  and  subtracted  in  the  same  manner 
as  whole  numbers.  The  decimal  points  must  be  kept  in  a 
vertical  line  and  the  other  figures  in  their  proper  columns. 

Add: 

1.  2.7;  .3;  37.1;  2.04;  .0033;  16.125;  105.06. 

2.  15.03;  325.075;  18.0025;  15.005;  87.08. 

3.  .0025;  .009;  .00125;  .875;  .05. 

4.  .425;  3.1416;  1.4142;  15.375;  8.8736;  5.75. 

5.  45.375;  37.525;  29.65;  86.245;  18.0005;  57.075. 

6.  .0075;  5.0035;  .2508;  .025;  2.1754;  .7856. 

7.  3.006;  61.375;  25.025;  7.75;  .0725;  15.7. 

8.  25.5;  5.78;  .375;  2.14;  37.45;  4.806;  8.6. 

9.  .625;  .375;  .875;  .125;  .75;  .25;  .075. 
10.  4.5;  67.34;  8.054;  .4862;  325.8;  .755. 
Subtract: 

1.  4.312  from  7.505.  6.  87.45  from  148.1. 

2.  1.4142  from  3.1416.  7.  29.802  from  32. 

3.  23.075  from  28.008.  8.  .25  from  25.1. 

4.  1.387  from  2.025.  9.  2.62  from  4.875. 
6.  5.75  from  11.025.  10.  27.51  from  30. 

Note:  Practice  should  be  given  in  reading  decimals  as  follows: 
1.4142 — read:  one,  point,  four,  one,  four,  two. 

Exercise  12.    Multiplication  of  Decimals 

Express  the  decimal  .05  as  a  common  fraction. 
Also  the  decimal  .5  as  a  common  fraction. 


REVIEW  OF  DECIMALS 


41 


If  we  multiply  two^^  without  cancelling,  what  is  the 
product? 

How  do  we  express  looo^  ^  decimal? 

Therefore:  If  we  multiply  .05  by  .5,  the  product  is  .025. 

How  does  the  number  of  decimal  places  in  the  product 
compare  with  the  number  of  decimal  places  in  both  the  multi- 
plicand and  multiplier? 

PRINCIPLE:  In  multiplication  of  decimals  as  many  places 
are  pointed  off  in  the  product  as  there  are  decimal  places 
in  both  multiplicand  and  multiplier.         £-  ,    Z  i'     t    y  i 


Multiply: 

1.  25.5X4.025 

2.  .005 X. 25 

3.  3.75X3.78 

4.  4.002 X. 32 
6.  .866X1.4 

6.  273.5X1.64 

7.  352.x. 0175 

8.  .0002 X. 0021 


/a 


i/-v1^ 


19.^-^0 


9.  62.5X7.05 

10.  .21 X. 3 

11.  $145.50X.375 

12.  $257.75 X. 06 

13.  $1250. X. 055 
1^.  2.72 X. 08 

15.  .0385 X. 55 

16.  6.45X3.83 


17.  $250. X. 055 

18.  275.5 X. 039 

19.  $272.75 X. 0275 

20.  7.5X3.1416 

21.  2.54X2.54 

22.  .5326X175.65 

23.  .0375 X. 0025 

24.  855.x. 0075 


25.  A  cubic  foot  of  water  weighs  approximately  62.5  pounds. 
Copper  is  8.93  times  as  heavy  as  the  same  volume  of  water. 
How  much  will  a  cubic  foot  of  copper  weigh? 

26.  Gold  is  19.3  times  as  heavy  as  the  same  volume  of  water. 
Find  the  weight  of  a  cubic  foot  of  gold. 

27.  How  much  heavier  is  a  cubic  foot  of  gold  than  a  cubic 
foot  of  copper? 

28.  A  gallon  of  water  weighs  8.34  pounds.  Kerosene  is  .8  as 
heavy  as  the  same  volume  of  water.  What  is  the  weight  of  a 
gallon  of  kerosene? 


42  SEVENTH  YEAR 

Exercise  13.    Applied  Problems 

U.  S.  Army  Daily  (Garrison)  Ration  per  Man 

Beef,  fresh 20.      oz.  Milk,  evap.  unsweetened.  .0.5  oz. 

Flour 18.      oz.  Vinegari 0.64  oz. 

Baking  powder 0.08  oz.  Salt 0.64  oz. 

Beans 2.4    oz.  Pepper,  black 0.04  oz. 

Potatoes 20.      oz.  Cinnamon 0.014  oz. 

Prunes 1.28  oz.  Lard 0.64  oz. 

Coffee,  roasted  and  ground.  1.12  oz.  Butter 0.5  oz. 

Sugar 3.2    oz.  Syrup 1.28  oz. 

Flavoring  extract,  lemon.  .0.014  oz. 

1.  Copy  in  column  form  and  find  the  total  weight,  in  pounds 
and  ounces,  of  the  seventeen  items  given  in  this  table. 

2.  Find  the  total  required  for  one  week.    For  thirty  days. 

3.  Find  from  local  prices  what  the  daily  ration  would  cost 
for  each  soldier.  Find  the  cost  per  day  for  a  company  of  195 
men. 

4.  Does  it  cost  the  government  as  much  to  feed  the  soldiers 
as  it  would  if  they  bought  their  supplies  at  your  local  stores? 
Why? 

5.  How  many  ounces  of  beef,  flour,  and  potatoes  are  required 
for  each  soldier  per  day? 

6.  How  many  ounces  of  beef,  flour,  and  potatoes  are  required 
per  day  for  a  regiment  of  1980  men?     How  many  pounds? 

7.  It  took  47  army  engineers  14  days  to  build  a  bridge. 
What  amount  of  rations  did  they  require  for  that  time? 

8.  Five  Signal  Service  Corps  men  were  stationed  21  days  at 
Mt.  View.     How  much  sugar  did  they  use  during  that  time? 

9.  Find  the  amount  of  salt  used  by  a  regiment  of  1980  men 
in  a  day?    Express  the  result  in  pounds  and  ounces. 

10.  How  much  butter  do  1980  soldiers  use  per  day? 

^Approximate  reduction  to  ounces.     The  government  standard  gives 
vinegar  0.16  gill  and  syrup  0.32  gill. 


r3^  x-.-^   . 

REVIEW  OF  DECIMALS  43 

Exercise  14.    Division  of  Decimals 

1.  Divide  .025  by  .05.  '  .    ''' 

Express  as  common  fractions  and  divide.     What  is  the 
quotient?    Express  this  quotient  as  a  decimal. 

Divide  the  following  decimals  by  using  common  fractions: 

2.  .625-M2.5.      X    r-i    "    ~T    ±1^^  ^  U- 

3.  .625-^.125.  P   v/ j^  . 

1^,  ,^^^^ 
Check  your  results  secured  by  dividing  wifH  common  frac- 
tions with  the  quotients  expressed  in  the  decimal  form  as 
shown  below: 

.5  .05  5 


.05)  .02  5  12. 5). 6  25  .125).  625 

25  6  25  625 

Answer  the  following  questions  for  each  of  the  above  prob- 
lems: 

4.  How  many  decimal  places  are  there  in  the  divisor? 

6.  How  many  decimal  places  is  the  decimal  point  in  the 
quotient  to  the  right  of  the  decimal  point  in  the  dividend? 

6.  Can  you  tell  from  the  above  problems  how  the  quotient 
should  be  pointed  off  in  the  division  of  decimals? 

PRINCIPLE:  In  division  of  decimals,  as  many  decimal  places 
are  pointed  oS  in  the  quotient  to  the  right  of  the  decimal 
point  in  the  dividend  as  there  are  decimal  places  in  the 
divisor. 

Caution:  Be  sure  that  you  place  the  figures  of  the  quotient 
exactly  where  they  belong  or  you  will  introduce  an  error  in 
the  result  when  you  point  off  the  decimal  places  in  the  quotient. 

Divide  the  following  (carry  out  three  decimal  places  if  they 
do  not  come  out  even) :  ^ 


44  SEVENTH  YEAR 

1.  30.  by  7.5  6.  31.042  by  8.3  11.  26.52  by  3.4 

2.  1.2  by  .6  7.  8.2  by  .0041  12.  20.5  by  8.2 

3.  36.  by  2.4  8.  46.875  by  .375  13.  8.5  by  3.4 

4.  51.165  by  37.9  9.  .0003  by  .5  14.  6.3  by  .18 

5.  .008  by  .04  10.  .4  by  .002  15.  3.  by  8 

Exercise  15.    Changing  a  Common  Fraction  to  a  Decimal 

On  page  23  it  was  shown  that  one  meaning  of  a  fraction  is: 
the  numerator  divided  by  the  denominator.  This  is  the  simplest 
method  to  use  in  reducing  a  common  fraction  to  a  decimal. 

Reduce  f  to  a  decimal.     Divide  3  by  8. 
.375 
8)3.000  Therefore:  f  =  .375 

Reduce  the  following  fractions  to  decimals: 

1.  2  6.   g  11.   g  16.  y 

2.  "3  7.  -g  12.   5  17.  -9 


3  8*   4  ^3-   5  ^8*   9 


4.  i  9.  i  14.  f  19.^ 

5.  t  10.  i  15.  I  20.^ 


Exercise  16.     Changing  a  Decimal  to  a  Common  Fraction 


Express  the  decimal  ,375  as  a  common  fraction.     Reduce 
is  fraction  to  its  lowest  terms.    Example:  iVo^o~^^~  §• 
Reduce  to  common  fractions: 


1. 

.50 

6. 

.6 

11. 

.125 

16. 

.05 

2. 

.625 

7. 

.875 

12. 

.2 

17. 

.075 

3. 

.75 

8. 

.03125 

13. 

.33i 

18. 

.025 

4. 

.8 

9. 

.0125 

14. 

.66f 

19. 

.02 

6. 

.25 

10. 

.0375 

16. 

.16i 

20. 

.35 

APPLIED  PROBLEMS  IN  FRACTIONS 


45 


Applied  Problems  Involving  Fractions 

The  following  problems  were  supplied  by  one  of  the  largest 
stores  in  the  United  States.  They  are  practical  problems, 
representing  selections  from  actual  sales  slips,  involving  frac- 
tions. Many  of  the  great  commercial  houses  find  it  necessary 
to  train  their  applicants  in  such  problems  as  these  in  order  to 
make  them  proficient  in  fractions. 

One  young  man  graduated  from  a  school  for  training  em- 
ployees in  a  half -day.  Why?  Simply  because  he  had  mastered 
his  arithmetic  before  applying  for  a  position  and  so  did  not 
need  the  course  of  training. 


Exercise  17 

Find  the  amount  of  the  purchases  in  each  of  the  following 
problems.     (Data  and  prices  for  1916): 

1.  Mrs.  H.  A.  Marshall  purchased  9f  yards  broadcloth  at 
$2.75  per  yard. 

2.  Mrs.  S.  A.  Thompson  bought  ij  yards  tulle  at  $2.75 
per  yard. 

3.  Miss  Myrtle  Hanlon  purchased  1^  yards  net  at  55j!f; 
1§  yards  lace  at  30^;  1  j  yards  veiling  at  $L75. 


46  SEVENTH  YEAR 

4.  Mrs.  Harry  Smith  bought  2f  yards  lace  at  65^;  2f  yards 
edging  at  3^;  8|  yards  edging  at  3^;  1  j  yards  edging  at  15^. 

5.  Mrs.  C.  P.  Murray  purchased  1^  yards  velour  at  $2.50; 
l|  yards  velvet  at  $3.50. 

6.  Mrs.  M.  M.  Spaulding  bought  5^  yards  dress  goods  at 
$2.65;  4f  yards  dress  goods  at  $3.55;  2j  yards  dress  goods  at 
$6.00;  3^  yards  dress  goods  at  $5.35. 

7.  Mrs.  E.  F.  Chatfield  ordered  6f  yards  lace  at  45^; 
Ij  yards  veiling  at  95^;  1  j  yards  fillet  at  55^;  ^  yard  net  at 
$1.95. 

8.  Mrs.  R.  F.  Arnold  purchased  5^  yards  edging  at  12)if; 
2  J  yards  silk  at  85^;  1§  yards  cretonne  at  $1.50;  ^  yard  damask 
at  15f^. 

9.  Mr.  C.  P.  Chase  purchased  the  following:  31 J  yards 
linoleum  at  $1.40;  81^  feet  wood  strips,  laid,  at  5^ff;  6f  yards 
cork  carpet  at  $1.25;  2f  dozen  f-inch  Daisy  pads  at  80f^. 

10.  Mrs.  R.  H.  Byron  purchased  ^  dozen  tassels  at  $9.00 
per  dozen;  if  yards  braid  at  QO^;  Ij  yards  guimpe  at  $1.75; 
1 2  yards  trimming  at  45^. 

11.  Mr.  S.  E.  Brown  bought  1 J  dozen  stair  pads  at  $2.00; 
21  f  yards  china  matting  at  40^;  6f  yards  Armstrong  linoleum 
at  $1.75. 

12.  Mr.  H.  H.  Howard  purchased  if  yards  linoleum  at  80^; 
1  Duchess  rug  at  $7.50;  1  Bokhara  rug  at  $35.00;  1  Smyrna 
rug  at  $7.00;  11  f  yards  velvet  stair  carpet  at  $1.35. 

13.  Mrs.  F.  A.  Cornell  made  the  following  purchases:  6f 
yards  guimpe  at  45c5;  f  dozen  tassels  at  $2.25;  4f  yards  fringe 
at  $1.75. 

14.  Mrs.  M.  H.  Gardner  bought  ^  dozen  tassels  at  75«f; 
3|-  yards  trimming  at  $1.05;  5f  yards  braid  at  50f5;  1  j  yards 
braid  at  $1.25. 


APPLIED  PROBLEMS  IN  FRACTIONS  47 

15.  Mrs.  J.  C.  Gibson  gave  the  following  order:  1^  yards 
fringe  at  10^;  2 1-  yards  trimming  at  25^;  3  j  yards  braid  at  50?^. 

16.  Mrs.  E.  S.  Harding  purchased  15^  yards  cretonne  at 
60^;  f  yard  taffeta  at  $2.50;  1  velour  remnant  at  $1.50. 

17.  Mrs.  F.  L.  Black  bought  |  yard  braid  at  75^;  2|  yards 
swansdown  at  $1.75;  l|  yards  trimming  at  18^. 

18.  Mr.  Frank  Adams  purchased  ^  dozen  rolls  paper  at 
12f!^  each;  f  yards  oil  cloth  at  30^;  if  yards  art  paper  at  25jif; 
f  dozen  Dutch  Klenzer  at  90ff. 

19.  Mrs.  Chas.  Madison  made  the  following  purchases: 
f  yards  oil  cloth  at  65^;  17^  yards  lace  at  5^;  ^  dozen  bars 
Ivory  Soap  at  84 j!^:  ^  dozen  cans  Kitchen  Klenzer  at  50(2^. 

20.  Mrs.  M.  C.  Nelson  bought  2 J  yards  net  at  $2.50;  ij 
yards  muslin  at  $2.50;  16f  yards  net  at  35^;  1^  yards  Sunfast 
at  $2.25;  ^  pair  portieres  at  $21.50. 

21.  Mrs.  Harry  Newell  bought  the  following  items:  7^ 
yards  Sundour  at  $2.50;  4^  yards  edging  at  lOjzf;  12^  yards 
muslin  at  40^. 

22.  Mrs.  D.  D.  Penfield  gave  the  following  order:  f  dozen 
towels  at  $3.00;  f  yards  damask  at  $1.50;  ^  dozen  wash  cloths 
at  $1.00;  §  dozen  dusters  at  $1.75. 

23.  Mrs.  C.  H.  Van  Buren  bought  the  following:  f  yards 
sheeting  at  75^;  ^  dozen  towels  at  $6.00;  ^  yard  linen  at  65ff; 
§  yard  linen  at  $1.25. 

24.  Mrs.  C.  P.  Warren  purchased  as  follows:  ^  dozen 
broom  bags  at  $2.40;  3^  yards  crash  at  30jzf;  2§  yards  huck 
at  55fi;  3§  yards  linen  at  Q5^. 

25.  Mrs.  Harry  S.  Perry  purchased  the  following:  ^  pound 
candy  at  40^;  2^  yards  embroidery  at  15j^;  4f  yards  embroidery 
at  15^;  if  yards  embroidery  at  18^. 


48  SEVENTH  YEAR 

26.  Mrs.  Wm.  Penn  bought  the  following:  1^  yarrds  silk 
at  $2.00;  Ij  yards  silk  crepe  at  $2.00;  l|  yards  silk  at  $1.00; 
f  yards  silk  net  at  $1.10. 

27.  Mrs.  O.  O.  Morrison  gave  the  following  order:  f  yards 
silk  at  $1.75;  9  yards  silk  poplin  at  50^;  1^  yards  silk  at  $1.75; 
f  yards  crepe  at  $1.50;  1§  yards  silk  at  75^. 

28.  Mrs.  S.  S.  Melrose  bought  as  follows:  2^  yards  ribbon 
at  28^;  2^  yards  ribbon  at  29^;  if  yards  ribbon  at  7jii;  4f  yards 
ribbon  at  14^. 

29.  Mrs.  Charles  Mason  purchased  the  following:  2  j  yards 
ribbon  at  25^;  3  j  yards  ribbon  at  18^;  1^  yards  ribbon  at  38^5; 
I  yard  ribbon  at  38^. 

30.  Mrs.  Chas.  P.  Hulce  ordered  2|-  yards  trimming  at  85^; 
f  yards  trimming  at  $3.00;  2j  yards  braid  at  50f^;4|  yards 
braid  at  7^;  if  yards  cord  at  S^. 

81.  Miss  T.  E.  Bennett  made  the  following  purchases:  if 
yards  edging  at  7^;  2f  yards  lace  at  4)^;  1^  yards  lace  at  60^; 
if  yards  lace  at  25^ 

32.  Mrs.  Harold  P.  Piatt  bought  the  following:  j  yard  dress 
goods  at  $3.10;  f  yards  dress  goods  at  65j^;  j  yard  dress  goods 
at  $3.25;  J  yard  dress  goods  at  $3.50. 

33.  Mrs.  C.  F.  Prince  ordered  the  following:  l|  yards  silver 
lace  at  $4.65;  lOf  yards  lace  at  $2.95;  2ff  yards  lace  at  $3.50; 
12j  yards  lace  at  $1.50;  |  yards  veiling  at  50fi. 

34.  Miss  S.  A.  Roberts  bought  ij  yards  braid  at  $1.65;  4j 
yards  braid  at  15^;  4f  yards  braid  at  3^;  8f  yards  braid  at  lOjZ^; 
if  yards  braid  at  $1.50. 

35.  Mrs.  C.  F.  Sheldon  purchased  16 j  yards  net  at  50^; 
3f  yards  muslin  at  55^;  44}  yards  net  at  $1.00;  2f  yards  net 
at  $1.25;  2f  yards  Sundour  at  $1.25. 


CHAPTER  III 

PERCENTAGE 

Exercise  1 

The  expression  per  cent  means  hundredths.  To  say  that 
4  per  cent  of  a  certain  cow's  milk  is  butter  fat  means  that 
Y^  of  the  milk  is  butter  fat.  The  sign  %  is  usually  used  in 
place  of  the  words  per  cent. 

The  fraction  twenty-five  hundredths  may  be  expressed  in 
three  ways:  (1)  as  a  common  fraction,  ^^;  (2)  as  a  decimal, 
.25;  (3)  as  a  per  cent,  25%.  The  name  hundredths  is  expressed 
in  the  first  case  by  the  denominator  100;  in  the  second  case 
by  means  of  the  decimal  point  and  the  two  decimal  places; 
and  in  the  third  case  by  the  sign  %. 

It  is  customary  to  omit  the  decimal  point  after  whole  numbers.  The 
decimal  point  is  placed  in  the  expression  25.%  to  make  clear  the  process 
of  changing  from  decimals  to  per  cent. 

How  has  the  decimal  point  been  moved  in  changing  from 
the  decimal  0.25  to  the  expression  25.%? 

A  decimal,  then,  may  be  changed  to  a  per  cent  by  moving 
the  decimal  point  two  places  to  the  right  and  attaching  the 
%  sign. 

Change  the  following  decimals  to  per  cents: 

1.  .25  6.  .125  11.  .75  16.  .3 

2.  .35  7.  .875  12.  .005  17.  .025 

3.  .01  8.  .5  13.  .00125  18.  .0075 

4.  .2  9.  .625  14.  2.5  19.  .85 

5.  .16|  10.  .375  16.  3.75  20.  .20 

49 


50 


SEVENTH  YEAR 


We  have   already   shown    that    25.%  =  .25.      In    changing 
from  %  to  a  decimal,  how  is  the  decimal  point  moved? 

Change  the  following  per  cents  to  decimals: 


1.  20% 

6.  25% 

11.  250% 

16.  50% 

2.  331% 

7.  .25% 

12.  625% 

17.  37^% 

3.  375%, 

8.  75% 

13.  10% 

18.  i% 

4.  12i% 

9.  62|% 

14.  66|% 

19.  lf% 

5.  .12|% 

10.  40% 

15.  60% 

20.  3.9% 

Exercise  2 

How  do  you  change  a  common  fraction  to  a  decimal?    Change 
the  following  fractions  to  decimals  and  then  to  per  cents  as 


follows:    -^=.05  =  ^ 


6. 
7. 
8. 
9. 
10. 


11. 
12. 
13. 
14. 
15. 


16. 
17. 
18. 
19. 
20. 


3 

4 

2 

3 

5 

6 

1 
16 

1 
60 


From  the  results  that  you  have  secured  in  the  above  exercise, 
fill  out  a  table  similar  to  the  form  shown  below.  Learn  all  the 
%  equivalents  of  the  common  fractions,  for  you  will  need  this 
information  in  the  following  exercise. 


Common  Fractions  and  Their  Equivalent  Per  Cents 


i=?% 

i=?% 

i=?% 

!=?% 

4=?% 

i=?% 

!=?% 

S=?% 

Have  the  teacher  check  this  table  before  you  learn  it  so  that  you  will 
not  learn  any  incorrect  equivalents. 


•     PERCENTAGE  51 

Exercise  3 

Find  12  J%  of  64.    12i%  =  what  common  fraction? 

If  we  know  that  12§%  =  |^,  which  is  easier,  to  take  .12^X64 
or  J  of  64? 

Find  the  following  per  cents  by  using  fractional  equivalents: 

1.  33i%  of  120  13.  75%  of  320 

2.  87 i%  of  160  14.  66f  %  of  300 

3.  25%  of  60  15.  16|%  of  96 

4.  20%  of  45  16.  83|%  of  36 
6.  37  J%  of  200  17.  2%  of  150 

6.  50%  of  1640  18.  80%  of  60 

7.  12  J%  of  400  19.  60%  of  450 

8.  ll|-%  of  81  20.  25%  of  820 

9.  62  J%  of  72  21.  141%,  of  70 

10.  40%  of  75  22.  37i%  of  16 

11.  10%  of  150  23.  33f  %  of  63 
.-^^- 12.  6f  %  of  30  24.  50%  of  84 

Since  per  cents  may  be  expressed  in  equivalent  decimals,  it 
is  often  convenient  to  multiply  by  a  decimal  if  the  fractional 
equivalent  is  large. 

Find  the  following  per  cents,  using  decimal  multipliers: 

25.  17%  of  153  31.     6%  of    43 

26.  23%  of    90  32.    7%  of    55 

27.  52%  of    83  33.  11%  of    85 

28.  37%  of  135  34.  15%  of  124 

29.  29%  of  105  35.  21%  of    34 

30.  16%  of    38  86.  .5%  of    96 

37.  Find  5^%  of  $2000. 

38.  Which  is  larger,  17%  of  $35  or  15%  of  $39? 


52  SEVENTH   YEAR 

Exercise  4 

Choose  the  most  convenient  equivalent  and  find  the  following 
per  cents: 

-2r  1.  25%  of  1240  16.  21%  of  825 

2.  8%  of  412  17.  40%  of  150 

3.  12%  of  217  18.  50%  of  842 
-i'  4.  20%  of  315  19.  16%  of  124 
^  5.  12§%  of  720  20.  87i%  of  128 
-i  6.  16f  %  of  96  21.  2%  of  500 

7.  22%  of  121  22.  7%  of  125 

8.  5%  of  132  23.  60%  of  $80 


9.  5%  of  120  24.  33§%  of 

10.  80%  of  250  25.  11^%  of  $450 

11.  13%  of  138  26.  75%  of  $480 

12.  37  J%  of  88  27.  17%  of  $312 

13.  66|%  of  75  28.  6%  of  $450 

14.  15%  of  200  29.  5|%  of  $110 

15.  62i%  of  160  30.  1  J%  of  $50 


.-*^\  EQUATIONS 

C    ^  Exercise  5 


1.  What  is  the  product  of  9X15?    9  and  15  are  called  the 
factors  of  the  product,  135. 

2.  If  the  two  factors  are  given,  what  process  is  used  in 
finding  the  product? 

3.  If  8  times  a  certain  number  =128,  what  is  the  number? 

4.  If  5  times  a  certain  number  =  55,  what  is  the  number? 

5.  If  the  product  of  two  factors =48  and  one  of  the  factors 
is  6,  what  is  the  other  factor? 


PERCENTAGE— THE  EQUATION       53 

6.  If  the  product  of  two  factors  is  91  and  one  of  the  factors 
is  13,  what  is  the  other  factor? 

7.  If  the  product  of  two  factors  and  one  of  the  factors  are 
given,  what  process  is  used  to  find  the  other  factor? 

Show  how  the  preceding  problems  illustrate  the  principles : 

1.  Factor  X  factor = product. 

2.  Product  -T-  one  factor  =  the  other  factor. 

The  letter  X  is  often  used  to  stand  for  the  unknown  product 
or  the  unknown  factor.  It  is  shorter  and  is  not  confusing  if 
you  remember  that  it  always  stands  for  the  unknown  number. 

Such  expressions  as  9X15  =  X  and  8XX=128  are  called 
equations  because  the  expressions  on  the  left  and  right  sides 
of  the  equality  sign  are  equal. 


-^  ^ 


Any  equation  can  be  represented  by  a  balance  as  shown  in  the 
illustration  above,  putting  the  expressions  on  the  scale  pans  and 
thus  showing  their  equality.  The  value  of  X  in  the  equation 
9  X 15  =  X  can  be  found  by  multiplying  the  two  factors  9  and  15. 
The  value  X  in  the  equation  8XX=128  is  found  by  dividing 
the  product  128  by  the  factor  8,  giving  the  other  factor  X=  16. 

Find  the  values  of  X  in  the  following  equations : 

1.  7XX=35  3.  .06X300  =  X 

2.  X  =  9X25  4.  .25XX  =  50 


54  SEVENTH  YEAR 

6.  XX 15  =  75  9.  40  =  XX 500 

6.  X=12X20  10.  6% X $150  =  X 

7.  12XX  =  240  11.  25%XX  =  $40 

8.  240  =  XX 20  12.  $16  =  X%XS200 

Exercise  6 

Percentage  problems  may  be  easily  solved  by  stating  them 
in  the  form  of  an  equation  and  then  solving  by  the  principles: 

1.  Factor  X  factor = product. 

2.  Product  -^  one  factor  =  the  other  factor. 

Remember  that,  in  multiplying  or  dividing,  per  cents  must  be  expressed 
either  as  decimals  or  as  common  fractions. 

1.  What  is  6%  of  $200? 

This  problem  may  easily  be  changed  into  an  equation.  X  may  stand 
for  what,  which  merely  stands  for  the  unknown  number.  Is  may  be 
replaced  by  the  equality  sign  ( = )  and  the  word  of  may  be  replaced  by 
the  sign  X.    The  equation  is: 

X  =  6%X$200. 

6%  and  $200  are  both  factors  of  the  unknown  product  X. 

The  principle  Factor  Xfactor  =  product  applies  to  this  equation.  Before 
we  multiply,  it  will  be  necessary  to  change  6%  to  a  decimal  or  a  common 
fraction  because  the  multiplier  must  be  an  abstract  number. 

6%  =  .06.    Therefore:  6%X$200  =  .06X$200  =  $12.00. 

2.  What  is  25%  of  $80? 

Equation:    X=25%X$80. 
25%=j.    Then25%X$80=|x$80  =  $20. 
State  the  equations  for  the  following  problems  and  then 
solve  them: 

3.  What  is  5%  of  $300?  8.  What  is  15%  of  $25? 

4.  What  is  10%  of  $120?  9.  What  is  60%  of  $350? 

5.  What  is  33|%  of  $90?  10.  What  is  8%  of  $110? 

6.  What  is  50%  of  22  pounds?   11.  What  is  16f  %  of  48  hogs? 

7.  What  is  20%  of  84  miles?       12.  What  is  12 §%  of  24  cents? 


PERCENTAGE— THE  EQUATION       55 

Exercise  (7y 

^,  A  boy  bought  a  motorcycle  for  $70  and  sold  it  at  a  gain 
of  20%.    How  much  did  he  gain? 

This  problem  can  be  changed  into  the  simple  form  of  the  preceding  exer- 
cise. The  question  is:  How  much  did  he  gain?  The  problem  states 
that  he  gained  20%.  Since  gain  is  always  figured  on  the  cost,  he  gained 
20%  of  $70.     In  short  form  the  problem  reaUy  means: 

What  is  20%  of  $70? 
Equation:    X=20%X$70. 

X  =  .20X$70  =  $14.00,  the  gain. 

Remember  that  the  number  of  per  cent  must  be  changed  to  a  decimal 
or  a  common  fraction  before  multiplying,  because  the  multipUer  must  be 
an  abstract  number. 

2.  A  merchant  sold  a  suit  costing  $15  at  a  profit  of  40%. 
What  was  his  profit  on  the  suit? 

By  studying  this  problem  as  we  did  problem  1,  we  see  that  it  can  be 
put  in  the  shortened  form: 

What  is  40%  of  $15? 

Equation:    X=40%X$15. 

40%  =|.    Then  X  =f  X$15  =  $6.00,  the  profit. 

3.  A  firm  recently  announced  an  increase  of  15%  in  the 
salaries  of  all  of  its  employees.  How  much  increase  would  a 
man  receive  whose  salary  had  been  $100  per  month? 

(j.  On  a  loan  of  $250  for  a  year,  I  receive  6%  of  that  sum 
for  the  use  of  the  money.  How  much  do  I  receive  for  the  use 
of  the  money? 

6.  A  real  estate  dealer  sold  a  lot  costing  $1500  at  a  gain  of 
33j%.    What  was  his  gain? 

Exercises  6  to  13  have  been  arranged  according  to  the  three  types  of 
percentage  problems  for  the  convenience  of  the  teacher  who  prefers  to  use 
a  different  method  from  the  one  developed  in  the  text. 


56  SEVENTH  YEAR 

6.  A  farmer  planted  40%  of  his  farm  of  240  acres  in  corn. 
How  many  acres  did  he  plant  in  corn? 

7.  A  ranch  owner  had  648  cattle  and  marketed  12 1%  of 
them.     How  many  cattle  did  he  market? 

'g)  An  agent  sold  an  automobile  costing  him  $1200  "at  a 
profit  of  33^%.     Find  the  amount  of  his  profit. 

9.  My  neighbor  sold  a  cow  costing  him  $75  at  a  gain  of 
20%.     Find  the  amount  of  his  profit. 

10.  I  have  a  balance  of  $150  on  deposit  in  the  bank.  If  I 
give  a  tailor  a  check  for  20%  of  this  amount  to  pay  for  a  suit  of 
clothes,  how  much  does  my  suit  cost  me? 

11.  A  grocer  sells  eggs  costing  36  cents  per  dozen  at  a  profit 
of  25%.  How  much  profit  does  he  make  on  each  dozen  of 
eggs? 

(^.  A  farmer  takes  a  can  containing  100  pounds  of  milk  to 
a  creamery.  A  test  is  made  of  the  milk  and  it  shows  that  the 
milk  contains  3.9%  of  butter  fat.  How  many  pounds  of  butter 
fat  are  there  in  the  can  of  milk? 

13.  A  family  pays  30%  of  their  income  of  $1200  for  rent. 
How  much  do  they  pay  for  rent? 

14.  At  what  price  must  a  horse  costing  $125  be  sold  to  gain 
for  its  owner  20%? 

15.  If  a  suit  marked  at  $25  is  reduced  20%  in  price,  v/hat  is 
the  reduced  price  mark? 

^§.  A  man  bought  4  suburban  lots  for  $700  each.  On  two 
of  them  he  made  a  gain  of  25%  when  he  sold  them  and  on  the 
others  he  lost  10%.    What  was  his  loss  or  gain  on  the  four  lots? 

The  last  three  problems  in  this  exercise  may  be  more  conveniently 
solved  by  using  the  method  shown  in  the  next  exercise. 


PERCENTAGE.  THE  EQUATION       57 


17.  How  much  yearly  interest  will  be  received  from  a 
Victory  Loan  Bond  at  4f  %  interest? 

18.  A  certain  city  has  a  population  of  10,500.  60%  of  the 
inhabitants  are  native  born,  18%  of  German  descent,  10%  of 
Irish  descent,  7%  of  Italian  descent,  and  the  remainder  of  other 
nationaUties.     How  many  of  each  group  are  there  in  this  city? 

19.  An  automobile  agent  bought  12  cars  and  sold  83§%  of 
them  during  the  first  month.  How  many  did  he  sell  during 
that  month?    How  many  did  he  have  left  out  of  the  12  cars? 

/io.  Elizabeth  saw  an  advertisement  of  a  special  sale  on  girls' 
coats.  All  coats  were  to  be  reduced  20%  of  the  former  prices. 
How  much  would  she  have  to  pay  for  a  coat  formerly  marked 
$28.50? 

21.  A  dry-goods  dealer  bought  a  supply  of  coats  at  $15  each. 
He  marked  tham  at  an  advance  of  80%.  What  was  the  marked 
price  of  the  coats? 

22.  A  seventh-grade  basket  ball  team  won  75%  of  the  games 
played.  If  this  team  played  8  games,  how  many  games  did 
they  win?    How  many  games  did  they  lose? 

23.  A  city  had  a  population  of  13,080  in  1910.  The  popula- 
tion in  1920  showed  an  increase  of  65%.  What  was  the  popu- 
lation of  this  city  in  1920? 

C^)  Real  estate  owners  estimate  that  an  apartment  or  a  house 
must  rent  for  10%  of  its  value  in  order  to  pay  for  repairs,  insur- 
ance, taxes,  and  a  fair  profit  on  the  investment.  What  should 
be  the  monthly  rent  on  a  house  costing  $6000  at  that  rate? 

26.  A  school  superintendent  received  a  salary  of  $3600  for  a 
term  of  10  months.  He  received  an  increase  of  25%  in  his 
salary.    What  was  his  new  salary  per  month? 

26.  Roy's  spelling  paper  was  marked  85%.  If  there  were  40 
words  in  the  test,  how  many  did  he  have  correct?  How  many 
did  he  have  wrong? 


58  SEVENTH  YEAR 

27.  A  merchant  sells  an  overcoat  for  $45.00.  His  profit  was 
40%  of  the  selling  price.     Find  the  profit. 

(^  Mrs.  Downer  rents  a  house  valued  at  $5250  for  a  year  at 
•8%  of  its  valuation.     Find  the  monthly  rent. 

29.  A  coal  dealer  raised  the  price  of  a  certain  grade  of  coal 
15%.  What  was  the  new  price  on  coal  formerly  selhng  at  $8.00 
per  ton? 

30.  A  cow  produced  262  pounds  of  milk  in  a  week  which  aver- 
aged 3.8%  butter  fat.  How  many  pounds  of  butter  fat  were 
there  in  her  milk  that  week  * 

31.  Mrs.  Griffin  receives  a  yearly  income  of  8%  on  an  invest- 
ment of  $3750.  How  much  is  her  monthly  income  from  that 
investment? 

®3^  What  should  be  the  monthly  rent  on  a  house  valued  at 
$4500  to  yield  a  return  of  10%  on  the  value  of  the  property? 

33.  A  school  had  an  enrollment  of  252  in  1919.  In  1920  the 
enrollment  increased  25%.     What  was  the  enrollment  in  1920? 

34.  A  merchant  bought  a  bill  of  goods  amounting  to  $3875.40. 

He  was  given  a  reduction  of  2%  for  paying  cash  for  the  goods. 

What  was  the  amount  of  the  reduction?    What  was  the  net 

amount  of  his  bill? 

r  ■ 

35.  A  regiment  consisting  of  2360  men  had  35%  of  its  men 

killed  or  wounded  in  a  battle.     How  many  men  were  left  unhurt 
out  of  the  regiment? 

Kae)  A  farmer  owed  $7250  on  his  farm.    He  paid  off  8%  of 
this  amount.    How  much  did  he  then  owe  on  the  farm? 

37.  In  a  city  grade  school  enrolling  1840  pupils,  45%  were 
boys.     How  many  girls  were  there  in  this  school? 

38.  Frank  sold  a  pair  of  roller  skates,  costing  $3,  for  83^%  of 
their  cost.    Find  the  seUing  price. 


'/ 


PERCENTAGE— THE  EQUATION  59 


jdkJif . 


Exercise  8 

1.  What  will  be  the  result  if  200  is  increased  12%  of  itself? 

200  is  already  100%  of  itself.  If  it  is  increased  12%,  the  result  will 
be  112%  of  200. 

Equation:     X  =  112%X200. 

X  =  1.12  X200  =  224.00,  the  new  result. 

2.  What  will  be  the  result  if  $125  is  decreased  20%? 
$125  =  100%  of  itself.     100%  -20%  (decrease)  =80%. 

The  new  result  will  be  only  80%  of  $125. 
X  =  80%X$125. 
X=|X$125=$100. 

What  will  be  the  result  if 

3.  300  is  increased  30%?  13.  $30  is  decreased  33j%? 

4.  $500  is  increased  6%?  14.  $250  is  decreased  20%? 

5.  180  lb.  is  increased  10%?  15.  360  is  decreased  10%? 

6.  $240  is  increased  16f  %?  16.  $75  is  decreased  20%? 

7.  80  is  increased  20%?  17.  40  is  decreased  40%? 

8.  36  is  increased  33  J%?  18.  240  bu.  is  decreased  12  J%? 

9.  160  lb.  is  increased  12  J%?  19.  140  lb.  is  decreased  10%? 

10.  20  bu.  is  increased  25%?       20.  $120  is  decreased  16|%? 

11.  $500  is  increased  8%?  21.  $80  is  decreased  37j%? 

12.  32  is  increased  25%?  22.  8  bu.  is  decreased  50%? 

23.  If  a  suit  of  clothes  marked  at  $30  is  reduced  16f  %  in 
price,  what  is  the  reduced  price  mark? 

24.  A  certain  brand  of  shoes,  retailing  at  $5  per  pair,  advanced 
20%  in  price  in  a  year.  What  was  the  increased  price  of  a  pair 
of  these  shoes? 

26.  A  man  paying  a  rental  of  $408  per  year  finds  that  his 
rent  is  to  be  increased  12%  on  account  of  improvements  on  the 
property.    What  is  his  new  rent  per  year? 


60  SEVENTH  YEAR 

26.  If  $1640  worth  of  groceries  have  advanced  25%  in  price 
since  they  were  purchased,  what  is  their  new  valuation? 

27.  A  man  has  $14,000  invested  in  a  lumber  business  and 
$26,000  in  an  artificial  stone  enterprise.  In  the  lumber  business, 
he  loses  8%  of  his  investment.  What  amount  must  he  gain  on 
the  other  investment  to  yield  him  a  profit  of  10%  on  both 
investments? 


Exercise  9 

1.  24  is  what  %  of  30? 
This  type  of  problem  may". easily  be  changed  into  the  equation  form: 

24=X%X30. 
In  this  equation  we  have  the  product  (24)  given  and  also  one  of  the 
factors  (30).    The  other  factor  is  unknown.    This  equation  involves  the 
principle: 

Product -hone  factor  =  the  bther  factor. 

.8  or  80% 

30)24.0 
24r0 
Therefore:  24  =  80%  of  30. 

2.  16  is  what  %  of  24? 

Equation:       16=X%X24. 
The  imknown  factor  X%  =  the  product  16 -j- the  factor  24. 
Since  a  fraction  may  stand  for  an  indicated  division,  we  may  indicate 
this  division  in  the  form  of  the  fraction,  -g-j. 

Then     X%=if  =  f  or66f%. 
Therefore :     16  is  66f  %  of  24. 

3.  6  is  ?%  of  18?  9.  $80  is  ?%  of  $120? 

4.  20  is  ?%,  of  25?  10.  24  bu.  is  ?%  of  40  bu.? 
6.  15  is  ?%  of  18?  11.  48  is  ?%  of  64? 

6.  25  is  ?%  of  40?  12.  $120  is  ?%  of  $2400? 

7.  48  is  ?%  of  80?  13.  $16  is  ?%,  of  $200? 

8.  27  is  ?%  of  36?  14.  20  bu.  is  ?%,  of  24  bu.? 


PERCENTAGE— PRACTICE  PROBLEMS  91 

15.  80  is  ?%  of  160?  22.  $400  is  ?%  of  $1200? 

16.  81  is  ?%  of  90?  23.  $63  is  ?%  of  $1260? 

17.  21  is  ?%  of  63?  24.  $7  is  ?%  of  $140? 

18.  24  is  ?%  of  240?  25.  $15  is  ?%  of  $300? 

19.  16  is  ?%  of  96?  26.  $12  is  ?%  of  $240? 

20.  75  is  ?%  of  125?  27.  320  acres  is  ?%  of  480  acres? 

21.  $60  is  ?%  of  $75?  28.  10  gallons  is  ?%  of  80  gallons? 

Work  of  this  type  is  valuable  in  giving  experience  in  solving  equations 
before  attempting  to  solve  concrete  problems  in  which  such  equations 
are  involved. 


Exercise  10 

1.  A  newsboy  bought  50  Sunday  papers  and  sold  48  of  them. 
What  per  dent  of  his  papers  did  he  sell? 

Since  he  sold  48  out  of  50,  the  question  is: 
48  is  what  %  of  50? 
Equation :    48 = X  %  X  50. 

PRINCIPLE:    Product -^ one  factor  =  the  other  factor. 

Then    X%=  48-;- 50  =  .96  or  96%. 

2.  A  farmer  bought  a  carload  of  steers  averaging  930  lb. 
When  the  farmer  sold  them,  they  averaged  1240  lb.  What 
was  the  per  cent  of  increase  in  their  weight? 

1240  lb.  -930  lb.  =310  lb.,  the  increase. 
310  lb.  is  what  %  of  930  lb.? 

3.  If  the  farmer  bought  the  steers  for  $9.75  per  hundred 
and  sold  them  for  $12.85  per  hundred,  what  was  his  per  cent 
of  gain  in  the  selling  price  per  hundred  over  the  buying  price? 

Q.  If  a  grocer  buys  eggs  at  36  cents  per  dozen  and  sells 
them  at  39  cents  per  dozen,  what  is  his  per  cent  of  profit? 

6.  During  the  season  of  1916,  the  Boston  American  League 
ball  team  won  91  games  out  of  a  total  of  154.  What  per  cent 
of  its  games  did  Boston  win? 


62  SEVENTH  YEAR 

6.  During  the  same  season,  Brooklyn  in  the  National 
League  won  94  games  out  of  154.  Find  the  per  cent  of  games 
won  by  Brooklyn. 

7.  In  the  World's  Series  between  Boston  and  Brooklyn, 
Boston  won  4  out  of  the  5  games  played.  What  per  cent  of 
games  did  Boston  win  in  this  series? 

8.  A  lumber  firm  increased  its  capital  from  $30,000  to 
$45,000.    What  was  the  per  cent  of  increase  in  its  capital? 

9.  A. laboratory  test  showed  that  a  white  potato,  weighing 
16  oz.,  contained  10  oz.  of  water.  What  is  the  per  cent  of  water 
in  potatoes  as  shown  by  this  test?  ' 

10.  The  same  kind  of  a  test  on  a  sweet  potato,  weighing 
15  oz.,  showed  that  it  contained  8.25  oz.  of  water.  What  per 
cent  of  water  is  there  in  a  sweet  potato?  J  / '  3 

11.  If  the  per  cent  of  refuse  is  the  same  in  both  white  and 
sweet  potatoes,  which  of  these  vegetables  contains  the  more 
nutritive  material? 

12.  If  sweet  potatoes  are  selling  at  4  cents  per  pound  and 
white  potatoes  at  2  cents  per  pound,  which  is  more  economical, 
considering  the  amount  of  nutritive  material  in  each? 

13.  What  per  cent  of  profit  must  be  made  on  the  sale  of 
goods  costing  $50,000  to  cover  an  expense  of  $7500  and  a  net' — 
gain  of  the  same  amount? 

14.  A  certain  grade  of  canned  peas  advanced  in  price  from 
12  cents  to  15  cents  per  can.    Find  the  per  cent  of  increase. 

15.  An  owner  of  a  bungalow  costing  $3000  rents  it  for  $25 
per  month.  His  expenses  are  $60  for  repairs,  taxes  and  insur- 
ance.   Find  the  per  cent  of  profit  each  year  on  his  investment. 

16.  A  farmer  applied  fertilizer  to  a  field  yielding  an  average 
of  48  bushels  of  corn  per  acre  and  secured  66  bushels  per  acre. 
Find  the  per  cent  of  increase  due  to  the  fertilizer. 


PERCENTAGE.    THE  EQUATION  63 

17.  A  teacher  bought  a  set  of  reference  books  for  $24,70  and 
sold  them  two  years  later  for  $15.00.  What  per  cent  did  they 
depreciate  in  value  in  the  two  years? 

18.  Erma  bought  a  pair  of  stockings  marked  75  cents  for  60 
cents  at  a  clearance  sale.  What  was  the  per  cent  of  reduction 
from  the  regular  price? 

19.  The  seventh  and  eighth  grades  of  a  village  school  had  a 
good  attendance  contest.  There  were  20  pupils  in  the  seventh 
grade  and  25  in  the  eighth  grade.  The  attendance  for  the  first 
week  was: 

7th  Grade  8th  Grade 

Monday 20  24 

Tuesday 20  23 

Wednesday 19  25 

Thursday •     18  25 

Friday 20  25 

What  was  the  average  per  cent  of  attendance  for  the  five  days 
'in  each  grade?    Which  grade  won  in  the  contest  that  week? 

20.  Fred  selected  8  ears  of  Golden  Bantam  sweet  corn  for 
seed.  He  took  10  grains  from  each  ear  and  tested  them.  Out 
of  the  total  number  tested  only  4  failed  to  grow.  What  was  the 
per  cent  of  grains  that  germinated? 

21.  In  a  spelling  test  Ruth  spelled  38  words  correctly  out  of  a 
list  of  40  words.  If  the  teacher  graded  in  per  cent  grades,  what 
should  have  been  her  grade — (scoring  all  the  words  equally)? 

22.  In  a  seventh  grade  spelling  test  of  50  words,  Helen  re- 
ceived the  highest  grade.  She  spelled  48  words  correctly.  What 
per  cent  of  the  list  did  she  have  right? 

23.  Many  cities  have  school  200  days  in  a  year.  What  per 
cent  of  a  year  (365  days)  is  the  school  term?  What  per  cent  is 
used  for  vacations? 


64  SEVENTH  YEAR 


/. 


24.  A  high  school  of  85  pupils  was  given  a  half -holiday  on  the 
Friday  following  the  end  of  the  month  if  the  attendance  was 
97%  or  more.  During  one  month  of  20  school  days  there  were 
82  half -days  of  absence.  What  was  the  per  cent  of  attendance? 
Was  the  school  entitled  to  a  half -holiday? 

26.  A  girl  bought  a  dress  priced  at  S25  for  $20  at  a  clearance 
sale.     What  was  the  per  cent  of  reduction? 

26.  A  bushel  of  corn  on  the  cob  weighs  70  pounds.  A  bushel 
of  shelled  corn  weighs  56  pounds.  The  weight  of  the  cobs  in  a 
bushel  of  ear  corn  is  what  per  cent  of  the  total  weight  of  a 
bushel  of  corn  on  the  cob? 

27.  Mrs.  Keith  set  an  incubator  with  144  eggs.  118  eggs 
hatched.     What  per  cent  of  the  eggs  hatched? 

28.  Donald  has  45  hens  and  gets  an  average  of  30  eggs  a  day 
during  the  spring.  What  is  the  average  per  cent  of  his  hens 
laying  each  day? 

29.  In  one  section  of  a  seventh  grade  there  are  12  girls  and 
9  boys.  What  per  cent  of  the  class  are  boys?  What  per  cent 
of  the  class  are  girls? 

30.  Compute  the  per  cents  of  boys  and  girls  for  your  class 
this  year. 

31.  A  landlord  rented  a  house  for  $45  per  month  for  a  year. 
His  expenses  for  taxes,  insurance,  and  repairs  amounted  to  $180. 
If  the  house  was  worth  $6000,  what  per  cent  of  the  value  of  the 
house  was  his  net  income? 

32.  The  population  of  Syracuse  in  1910  was  137,249.  In  1920 
the  population  was  171,647.  Find  the  per  cent  of  increase  for 
the  ten  years. 

33.  A  city  railway  company  reported  a  net  profit  of  $2.86  for 
each  $50  share.    What  was  the  per  cent  of  profit? 


I  (x^-^Tf    />^_^t--«-*-^*-v.'— V        /v        v-^^^'-'i-^    ,/ir  A.-«OCL/ 


PERCENTAGE— FRACTIONAL  EQUIVALENTS    65 


Exercise  11 

1.  24  is  75%  of  what  number? 

Equation:     24=75%XX. 

X,  the  unknown  factor,  =  24  -J-  .75  =  32. 

Care  must  be  taken  in  this  type  of  problem  to  reduce  the  per  cent  to 
a  decimal  or  a  common  fraction  before  dividing. 

2.  16  is  25%  of  what  number? 

Equation:     16  =  25%XX. 

In  this  problem,  we  see  that  16 =25%  or  j  of  the  number.  The  number 
=  4  times  16,  or  64. 

Fractional  equivalents  are  much  shorter  in  solving  some  equations  than 
decimals.  Practice  using  both  in  solving  equations  and  then  choose  the 
more  convenient  method  for  each  equation. 

3.  18  is  12  J%  of  ?  12.  $15  is  5%  of  ? 

4.  21  is  75%  of  ?  13.  $21  is  6%  of  ? 

5.  48  is  80%  of  ?  14.  $14  is  4%  of  ?     4  ./  »  /  #• 

6.  40  is  62i%  of  ?  15.  $12.80  is  8%  of  ? 

7.  8  is  16f  %  of  ?  16.  11  lb.  is  4%  of  ? 

8.  64  is  50%  of  ?  17.  9  is  2  J%  of  ?     ^i 

9.  12  is  25%  of  ?  18.  12  is  3%  of  ? 

10.  63  is  87  J%  of  ?  19.  245  is  20%  of  ? 

11.  9  is  16f  %  of  ?  20.  81  is  37^%  of  ? 


«  • 


Exercise  12 

1.  If  a  man  sells  a  house  for  $2760,  which  is  92%  of  what 
he  paid  for  it,  what  was  the  original  purchase  price? 

In  short  form  this  problem  means:    $2760  is  92%  of  ?  (cost). 
Equation:   $2760=92%XX. 
Find  the  value  of  X. 


66  SEVENTH  YEAR 

2.  I  wrote  a  check  for  an  insurance  premium  for  $52.24 
and  found  that  it  would  take  out  42%  of  the  money  I  had  on 
deposit  in  the  bank.    How  much  money  did  I  have  on  deposit? 

3.  After  losing  18%  of  his  investment  in  a  gold  mine,  a 
man  has  $6192.60  left.  How  much  did  he  have  invested  in 
the  mine? 

4.  A  farmer  sold  a  cow  for  $84,  thereby  gaining  20%. 
How  much  did  the  cow  cost? 

Suggestions:  The  cost  of  the  cow  =100%  of  the  cost. 
If  the  farmer  gained  20%,  he  sold  the  cow  for  how  many  %  of 
the  cost? 

6.  The  present  enrollment  of  a  school  of  486  pupils  is  20% 
more  than  its  last  year's  enrollment.  What  was  the  last  year's 
enrollment? 

6.  The  circulation  of  a  certain  newspaper  is  now  39,875. 
This  is  an  increase  of  10%  over  that  of  last  year.  What  was 
last  year's  circulation? 

7.  If  a  railway  line  has  been  extended  18%  of  its  original 
length  and  is  now  554.6  miles  long,  what  was  its  original  length? 

8.  If  I  add  to  my  bank  deposit  $120,  which  is  60%  of 
what  I  already  have  on  deposit,  what  was  my  balance  before 
making  the  deposit? 

9.  I  paid  $5  for  a  pair  of  shoes.  This  was  16f  %  of  what  I 
paid  for  a  suit.    How  much  did  I  pay  for  the  suit? 

10.  A  bank  distributes  dividends  amounting  to  $4800. 
This  sum  is  12%  of  its  capital  stock.    Find  its  capital  stock. 

11.  A  banker  gained  8%  on  an  investment.  If  his  profits 
were  $202,  what  was  the  amount  of  his  investment? 

12.  A  boy  gained  6  lb.  during  his  summer  vacation.  This 
was  6  j%  of  his  weight  at  the  beginning  of  the  vacation.  How 
much  did  he  weigh  at  the  close  of  the  vacation? 


PERCENTAGE.  THE  EQUATION       67 

Practice  Exercises  in  Percentage 

These  exercises  have  been  devised  to  give  practice  on  the 
various  processes  involved  in  percentage.  If  the  pupils  fail  to 
do  each  exercise  in  the  time  limit,  they  should  be  drilled  on  the 
facts  in  a  different  arrangement  until  they  can  reach  the  stand- 
ard time.  Hektograph  or  mimeograph  this  material  for  writ^^en 
practice  work.    Demand  100%  accuracy  for  each  exercise. 

Time  Limits  for  Written  Work 

Excellent — 1  min.     Good  1^  min.     Fair — 2  min. 

Exercise  A 

Change  the  following  decimals  to  per  cents: 


1—8 

9—16 

17- 

-24 

26—32 

.75     =  ?  % 

.725  =  ?  % 

.45 

=  ?% 

5.04     =  ?  % 

.06    =  ?  % 

.71     =  ?  % 

1.20 

=  ?% 

.425  =  ?  % 

.625  =  ?  % 

.675  =  ?  % 

.425 

=  ?% 

•6       =  ?  % 

.4      =  ?  % 

.35    =  ?  % 

.07 

=  ?% 

1.54     =  ?  % 

.035  =  ?  % 

.005  =  ?  % 

.375 

=  ?% 

.043  =  ?  % 

.33j  =  ?  % 

.025  =  ?  % 

.66i 

=  ?% 

3.8      =  ?  % 

2.52     =  ?  % 

.054  =  ?  % 

1.38 

=  •?% 

1.05     =  ?  % 

.225  =  ?  % 

.03     =  ?  % 

.7 

=  ?% 

.039  =  ?  % 

Exercise  B 

Change  to  per  cents: 

1—7 

8—14 

15- 

-21 

22—28       V^ 

i  =  ?% 

f  =  ?% 

7 
8    - 

=  ?% 

iV  =  ?  %  ^   ^^ 

i  =  ?% 

f  =  ?  % 

1^   = 

^?% 

iV  =  ?  %     < 

h  =  f% 

f  =  ?% 

i- 

^?% 

li  =  ?  %   ; 

i  =  ?% 

i  =  ?%^^! 

i  = 

^  ?% 

iV  =  ?  %  ^  V 

f  =  ?% 

t  =  ?%f>'> 

f  = 

^?% 

li  =  ?  % 

i  =  ?% 

f  =  ?% 

ih  = 

^?% 

A  =  ?% 

1  =  ?  % 

!  =  ?% 

A  = 

?% 

If  =  ?  % 

68 


SEVENTH  YEAR 


Exercise  C 


Change  to  common  fractions: 


1—7 

60  %  =  ? 

75  %  =  ? 
28f  %  =  ? 
5  %  =  ? 
33j%  =  ? 
25  %  =  ? 
90  %  =  ? 


8—14 

10  %  =  ?  , 
6f%  =  ? 
66|%  =  ? 
40  %  =  ?  ' 
87  J%  =  ? 
70  %  =  ? 
20  %  =  ? 


15—21 

30  %  =  ? 

12i%  =  ? 

6i%  =  ? 

16|%  =  ? 

lli%  =  ? 
83i%  =  ? 
50  %  =  ? 


Exercise  D 


Change  to  decimals: 


1—7 

32  %  =  ? 

50  %  =  ? 

125  %  =  ? 

3.9%  =  ? 

4f  %  =  ? 
25  %  =  ? 
62j%  =  ? 


8—14 

10  %  =  ? 

ii%  =  ? 

33i%  =  ? 
275  %  =  ? 

2  %  =  ? 

87i%  =  ? 

6  %  =  ? 


15—21 

80  %  =  ? 

105.5%  =  ? 

4.1%  =  ? 

250  %  =  ? 

21  %  =  ? 
175  %  =  ? 

5.25%  =  ? 


1.  6%X$375  =  ? 

2.  7%X  S50  =  ? 


1.  21%X$300  =  ? 

2.  3%X  $85  =  ? 


Exercise  E 

3.  11%X$600  =  ? 

4.  3.5%X$400  =  ? 
7.  4.1%X2001b.  =  ? 

Exercise  F 

3.  9%X$250  =  ? 

4.  18%  X  $230  =  ? 

7.  3.9%X2751b.  =  ? 


22—28 

62i%  =  i'^ 
125  %  =  ? 

37i%  =  ?  ^ 
150  %  =  ?  '  • 

14f%  =  ?\ 
175  %  =  ?\' 

80  %  =  ? 


22—28 

ii%  =  ? 

40  %  =  ? 
7.5%  =  ? 

If  %  =  ? 

42  %  =  ? 

.25%  =  ? 

4.9%  =  ? 


5„    8%X  $85  =  ? 
6.  15%X$160  =  ? 


6.     5%X3601b.  =  ? 
6.  32%X$300     =? 


In  hektographing  or  mimeographing  such  exercises  as  E  to  M,  leave 
space  enough  under  each  example  to  perform  the  solution. 


PRACTICE  EXERCISES  IN  PERCENTAGE        69 

Exercise  G 

1.  37i%X480  =  ?        3.  83j%X  54  =  ?         5.  12i%X808  =  ? 

2.  14f%X210  =  ?         4.  75  %X640  =  ?         6.  60  %X420  =  ? 

7.  25%X808  =  ?  8.  66f%X312  =  ? 

Exercise  H 

1.  62i%X840  =  ?        3.  40  %X520  =  ?         6.    6i%X  80  =  ? 

2.  16f%X984  =  ?        4.  11^%X639  =  ?         6.  70  %X190  =  ? 

7.  33i%X975  =  ?  8.  125%X240  =  ? 

Exercise  I 

Find  the  value  of  x  in  each  equation : 

1.  25  =  x%  X40  4.  64    =  a;%X96 

2.  12  =  3%  X  re  6.  120  =  75%  X  x 
Z.x=  12i%  X  64  6.  a:      =  6%  X  $250 

Exercise  J 

Find  the  value  of  x  in  each  equation : 

1.  400  =  8%  X  a;  4.  32  =  a:%  X  80 

2.  X      =  33j%  X  876  6.  a;    =  37^%  X  48 
8.  320  =  a;%  X  400                     6.  96  =  25%  X  :5 

Exercise  K 

State  equations  for  the  following  and  solve  each: 

1.  What  is  60%  of  $65? 

2.  $24  is  what  per  cent  of  $40?    ">  '  ^. 

3.  15  cents  is  37§%  of  what  amount?  3  - 

4.  What  is  83§%  of  $84?  'V  ' 

Exercise  L 

State  equations  for  the  following  and  solve  each: 

1.  What  is  62|%  of  $720? 

2.  $120  is  what  per  cent  of  $2400?    ^     ^  ^ 

3.  $640  is  40%  of  what  amount?    v  u^>, 

4.  What  is  6i%  of  $800?     ^; 


70  SEVENTH  YEAR 

Have  the  pupils  solve  the  following  list  of  percentage  problems 
as  a  speed  exercise.  Use  the  following  time  limits  for  this 
exercise : 

Excellent — 4  minutes.  Good — 6  minutes.  Fair — 8  minutes. 
Exercise  M 

1.  A  merchant  sold  a  suit  costing  $30  at  a  profit  of  40%. 
What  was  his  profit  on  the  suit? 

2.  A  newsboy  buys  papers  at  2  cents  each  and  sells  them  at 

3  cents  each.     What  is  his  per  cent  of  gain? 

3.  A  merchant's  expenses  for  operating  his  store  amount  to 
16f  %  of  his  yearly  sales.  If  he  sells  $36,630  worth  of  goods 
during  1920,  what  were  his  expenses  for  operating  his  store  that 
year? 

4.  A  boy  spent  33f  %  of  what  he  had  on  deposit  in  a  bank 
for  a  bicycle.  If  the  bicycle  cost  $42,  what  did  he  have  on 
deposit  before  he  bought  the  bicycle? 

5.  A  variety  store  buys  a  certain  toy  for  6  cents  each  and 
sells  it  for  10  cents.     Find  its  per  cent  of  profit  on  this  toy. 

6.  A  city  had  a  population  of  approximately  6000  in  1910. 
The  1920  census  showed  that  it  had  gained  25%  in  the  ten  years. 
Find  its  population  in  1920. 

7.  An  overcoat,  marked  $48,  was  sold  on  a  special  sale  at  a 
reduction  of  33^%.     What  was  the  selling  price? 

8.  What  is  the  per  cent  of  profit  on  an  article  bought  for 

4  cents  and  sold  for  10  cents? 

9.  A  real  estate  firm  rents  a  house  costing  $4800  so  that  it 
yields  a  return  of  10%  on  the  investment.  What  monthly 
rent  does  it  charge  for  this  house? 

10.  A  bookkeeper  working  on  a  salary  of  $120  per  month 
had  his  salary  increased  12^%.  What  was  the  yearly  increase 
in  his  salary? 

Encourage  pupils  to  work  every  problem  mentally  that  they  possibly 
can  and  merely  set  down  the  final  answer.  This  practice  should  be  fol- 
lowed in  every  exercise  in  this  book  as  well  as  in  speed  exercises. 


& 


PERCENTAGE— REVIEW  PROBLEMS  71 

REVIEW  PROBLEMS  IN  PERCENTAGE^ 
Exercise  13 

1.  Mr.  Brown  lost  15%  on  an  investment  of  $1800.  What 
was  his  loss? 

2.  A  boy  who  weighs  77  lb.  has  gained  10%  since  his  last 
birthday.    What  was  his  weight  then? 

3.  An  owner  of  a  farm  worth"  $175  an  acre  wishes  to  get 
a  return  of  4^%  on  his  investment.    What  rent  must  he  charge? 

4.  If  you  have  12  problems  to  solve  for  home  work  and  work 
10  correctly,  what  should  your  grade  be,  considering  the  prob- 
lems of  equal  value  in  grading? 

5.  23  pupils  in  a  class  of  25  were  promoted.  What  per  cent 
of  pupils  failed? 

6.  A  man  has  an  annual  income  of  $1500  and  pays  $420 
a  year  for  rent.  What  per  cent  of  his  income  does  he  pay  for 
rent? 

7.  A  liveryman  bought  a  team  of  horses  for  $350.  After 
using  them  for  two  years,  he  sold  them  at  a  loss  of  40%.  What 
did  he  receive  for  the  team? 

8.  A  contractor  figured  a  house  to  cost  $4375  and  secured 
the  contract  for  $5500.  What  was  his  per  cent  of  profit  if  his 
estimate  was  correct? 

9.  An  abandoned  beach  hotel  which  cost  $80,000  is  sold  for 
$48,000  at  what  per  cent  of  loss?  The  purchaser  reopens  it 
for  a  new  class  of  patronage  and  sells  it  to  a  company  for  the 
original  cost.    What  was  his  per  cent  of  profit? 

10.  A  boy  gave  his  playmates  75%  of  his  apples  and  had 
4  left.    How  many  had  he  at  first? 

^This  list  of  problems  is  designed  to  give  practice  in  stating  equations 
for  the  three  types  of  percentage  problems. 


72  SEVENTH  YEAR 

11.  A  teamster  paid  $100  each  for  2  horses,  $60  for  a  wagon, 
and  $20  for  ^  second-hand  set  of  harness.  At  what  price  must 
he  sell  the  outfit  to  gain  10%? 

12.  The  sales  of  a  certain  store  were  $72,000  for  the  year  and 
the  profit,  $8000.     Find  the  per  cent  of  profit  on  the  sales. 

13.  A  mill  is  sold  for  $856,000  at  an  advance  of  14y%  on 
its  cost  price.    How  much  did  it  cost? 

14.  A  man's  expenses  in  a  year  are  $1200.  His  salary  is 
133^%  of  that  amount.  How  much  money  can  he  save  in  a 
year  out  of  his  salary? 

16.  A  grocer  buys  eggs  at  wholesale  for  36^  and  sells  them 
for  4lO^  per  dozen.     What  is  his  per  cent  of  profit? 

16.  I  paid  my  rent  with  a  check  for  $37.50,  which  was  5% 
of  my  deposits  in  the  bank.  What  was  the  balance  remaining 
in  the  bank? 

17.  A  collector  charged  $60  for  collecting  a  debt  of  $1200. 
What  per  cent  did  he  charge  for  collecting? 

18.  The  engine  in  my  automobile  is  40  H.  P.  My  neighbor's 
engine  is  60  H.  P.  His  engine  is  how  many  per  cent  as  powerful 
as  mine? 

19.  A  factory  employing  40  equally  paid  operators  of 
machines,  reduces  its  force  by  25%  and  increases  by  25%  the 
wages  of  those  that  remain.  Does  it  pay  more  or  less  in  wages 
than  before? 

20.  Helen  spent  35%  of  her  Christmas  money  on  one  shop- 
ping trip  and  28%  on  the  next  trip.  What  per  cent  of  her  money 
was  left?  If  she  had  $7.40  left,  how  much  money  had  she  at 
first? 

21.  A  merchant  sold  goods  for  which  he  paid  $30,000  at  an 
average  of  30%  higher  price,  but  lost  5%  from  the  failure  of 
certain  debtors.    What  was  the  amount  of  his  profit? 


PERCENTAGE— PUPILS'  OWN  PROBLEMS        73 

22.  If  one  cow  yields  15  quarts  of  milk  each  day,  the  milk 
containing  3.5%  of  butter  fat,  and  another  cow  yields  12 
quarts  of  milk  per  day,  containing  4.5%  of  butter  fat,  which 
cow  is  the  more  profitable  for  butter  making? 

23.  A  house  and  lot  were  purchased  for  $4000.  The  house 
was  moved  and  sold  for  $2000  and  the  cost  of  moving.  At  what 
price  must  the  lot  be  sold  to  realize  a  total  gain  of  25%  on  the 
investment? 

24.  The  sales  in  a  store  were  $960  for  one  day,  which  would 
have  meant  a  profit  of  20%  but  for  the  unfortunate  acceptance 
of  a  counterfeit  20-dollar  bill  which  could  not  be  traced  to  the 
payer.    What  was  the  net  per  cent  of  gain? 

25.  Standard  milk  is  87%  water,  4%  fat,  .7%  ash,  3.3% 
protein  and  the  remainder  is  made  up  of  carbohydrates.  What 
per  cent  of  standard  milk  is  carbohydrates? 

26.  A  merchant  marks  a  suit  of  clothes  costing  $20  at  an 
increase  of  60%.  Later  he  discounts  the  marked  price  20%. 
What  was  the  cost  to  the  purchaser?  What  was  the  merchant's 
per  cent  of  profit  on  his  cost? 

27.  After  grooving,  a  4-inch  floor  board  is  only  3^  inches 
on  its  face.  If  you  figure  the  number  of  board  feet  for  a  floor, 
what  per  cent  must  you  add  to  allow  for  the  grooving? 

Exercise  14 
PROBLEMS  COLLECTED  BY  PUPILS 

The  following  problems  were  gathered  by  a  seventh  grade 
class  from  their  experiences  and  consultations  with  their 
parents.    See  how  many  of  these  problems  you  can  solve. 

1.  I  have  done  8  of  the  50  arithmetic  drill  cards.  What 
per  cent  have  I  yet  to  do? 

2.  My  father  received  an  order  from  the  army  for  $85,900 
worth  of  goods.  He  receives  4%  commission.  How  much 
does  he  receive? 


74  SEVENTH  YEAR 

3.  I  bought  a  share  of  stock  last  year  for  $114.  I  have  just 
sold  it  for  $181.    What  was  my  per  cent  of  gain? 

4.  Last  year  flour  was  $6.75  per  bbl.  and  this  year  (1916) 
it  is  $10.00  per  bbl.    What  is  the  per  cent  of  increase? 

6.  A  bill  of  lumber  was  sold,  the  price  being  $864,  but  an 
allowance  of  10%  was  made  for  poor  grade.  There  was  also 
a  discount  of  2%  for  prompt  payment.  Find  the  net  amount 
of  the  bill. 

6.  A  manufacturer  makes  and  sells  an  article  for  $24.00  per 
dozen.  His  overhead  charges^  are  20%  of  this  and  he  allows 
a  cash  discount  of  7%.  What  is  the  net  amount  of  his  profit 
per  dozen,  after  deducting  $15.00  for  materials  and  cost  of 
manufacturing? 

7.  A  wholesale  dealer  buys  a  boiler  from  the  manufacturer 
at  the  list  price  of  $24.00  less  40%  discount.  He  sells  it  to  his 
retail  customer  at  30%  discount  from  the  list  price.  How 
much  profit  does  he  make  on  the  sale? 

8.  A  corporation  is  capitalized  at  $50,000,  How  much  busi- 
ness will  they  have  to  do  yearly  to  pay  a  dividend  of  10%  on 
their  capital  stock,  provided  their  profit  is  5%  of  their  total 
sales? 

9.  During  1915  a  manufacturer  employed  206  men  at 
$2.00  per  day.  In  1916  he  employed  175  men  and  his  total 
daily  wage  bill  was  $395.00.  By  what  per  cent  had  the  daily 
per  capita  wage  increased? 

10.  In  1900,  $100  would  buy  a  certain  number  of  articles 
of  goods.  In  1910,  it  took  $120  to  buy  the  same  articles  and 
in  1916  it  took  $160  to  buy  the  same  goods.  By  what  per  cent 
should  wages  have  increased  between  1910  and  1916  to  have 
enabled  the  laborer  to  purchase  the  same  quantity  of  goods  in 
1916  as  he  had  been  able  to  purchase  in  1910? 

^Overhead  charges  cover  all  expenses  of  a  factory  except  cost  of  material 
and  cost  of  labor. 


PERCENTAGE— DAIRY  PRODUCTS 
Exercise  15 


75 


Prepare  a  list  of  percentage  problems  based  on  the  business 
conditions  in  your  community.  Each  pupil  should  bring  in 
at  least  two  problems  from  which  the  teacher  can  select  a  list 
for  review  work  in  percentage.  Try  to  get  actual  transactions 
to  use  in  your  problems. 


Exercise  16 

MILK  AND  CREAM 

Efficient  dairymen  are  now  testing 
the  milk  of  each  cow  to  see  which  are 
the  most  productive.  Those  which  are 
not  profitable  are  sold  and  others  secured 
in  their  places  which  produce  a  higher 
per  cent  of  butter  fat.  The  amount 
of  butter  fat  is  ascertained  by  means 
of  the  Babcock  test. 

1.  Some  pupil  in  the  class  should  make  a  careful  study  of 
the  Babcock  test  and  make  a  full  report  to  the  class. 

2.  Standard  milk  is  87%  water,  4%  fat,  3.3%  protein, 
.7%  ash,  and  the  remainder  is  made  up  of  carbohydrates. 
What  per  cent  of  standard  milk  is  carbohydrates? 

3.  Cream  is  74%  water,  2.5%  protein,  4.5%  carbohydrates, 
.5%  ash  and  the  remainder  fat.  What  per  cent  of  the  cream  is 
fat? 

The  test  for  butter  fat  is  made  in  bottles  similar 
to  the  one  shown  in  the  illustration.  The  butter  fat 
accumulates  in  the  neck  of  the  bottle  and  can  be 
measured  on  the  scale  with  a  pair  of  dividers.  The 
bottle  in  the  illustration  shows  a  test  yielding  4% 
of  butter  fat. 


76  SEVENTH  YEAR 

4.  A  farmer  took  a  can  of  milk  weighing  275  lb.  to  the 
creamery.  The  test  for  this  milk  showed  3.8%  of  butter  fat. 
How  much  did  he  receive  for  this  butter  fat  at  56  cents  per 
pound? 

6.  A  certain  recorded  Jersey  cow  yielded  17,557  pounds 
of  milk  in  one  year.  From  this  amount  of  milk,  998  pounds 
of  butter  fat  were  obtained.  What  per  cent  of  the  milk  was 
butter  fat? 

6.  A  certain  recorded  Guernsey  cow  yielded  in  one  year 
910  pounds  of  butter  fat  in  17,285  pounds  of  milk.  What  was 
the  per  cent  of  butter  fat  in  her  milk? 

7.  A  Shorthorn  cow  yielded  18,075  pounds  of  milk  in  a  year. 
The  milk  of  this  cow  contained  735  pounds  of  butter  fat. 
What  was  the  per  cent  of  butter  fat  in  her  milk? 

8.  A  cow's  milk  was  tested  by  a  dairyman  with  a  view  to 
purchasing  the  cow.  He  found  her  milk  to  test  3.2%  butter 
fat.  If  the  price  was  satisfactory,  would  you  buy  the  cow  to 
add  to  a  dairy  herd? 

9.  A  certain  Holstein  cow  yielded  an  average  of  14,134 
pounds  of  milk  per  year  for  five  years.  If  her  milk  tested 
3.7%  butter  fat,  how  many  pounds  of  butter  fat  did  this  cow 
produce  in  the  five  years? 

10.  How  much  was  this  butter  fat  worth  at  56  cents  per 
pound? 

11.  If  one  cow  yields  30  lb.  of  milk  per  day  testing  3.4% 
of  butter  fat  and  another  cow  yields  25  lb.  of  milk  testing 
4.4%  of  butter  fat,  which  cow  is  the  more  profitable  and  how 
much  per  week? 

If  whole  milk  is  sold  for  city  consumption,  the  quantity  of  milk  is  a 
more  important  consideration  than  the  per  cent  of  butter  fat,  providing 
that  the  percentage  of  butter  fat  does  not  fall  below  a  minimum  of  about 
3.4%. 


PERCENTAGE— DAIRY  PRODUCTS 


77 


12.  A  dairyman  tested  ten  cows  for  butter  fat  with  the 


following  results : 

Pounds  of  milk 

Per  cent  of 

Cow 

per  day 

butter  fat 

1 

30 

3.9 

2 

28 

3.4 

3 

24 

4.0 

4 

35 

4.1 

5 

26 

3.3 

6 

32 

3.9 

7 

22 

3.8 

8 

29 

4.2 

9 

21 

3.5 

10 

28 

4.0 

Which  cows  would  you  recommend  that  he  keep  and  which 
ones  would  you  recommend  that  he  sell  and  buy  others  to  take 
their  places?    Give  reasons  for  your  decisions. 

Duchess  Skylark  Ormsby, 
a  Holstein-Friesian  cow,  has 
the  record  of  being  the 
world's  champion  butter 
producer.  She  produced 
27,761  lb.  of  milk  in  a 
year,  yielding  1205  lb.  of 
butter  fat. 

13.  Find  the  per  cent 
of  butter  fat  in  the  milk  of 
the  champion  cow. 

14.  At  35  cents  a  pound,  how  much  was  that  amount  of 
butter  fat  worth? 

15.  How  much  would  the  whole  milk  from  this  cow  have 
brought  at  $2.00  per  hundred  pounds? 


■"  ."-    ^v-^ 

i&tJ^     '•    "Jb 

Hill         I'lTfc     1     /r     r     ~,^::^iil 

HI 

'  ^ 

k 

Courtesy  of  the  International  Harvester  Co. 


78 


SEVENTH  YEAR 


THE  MEAT  INDUSTRY 

(Applied  percentage  problems) 


|^si^w«»«^S 


The  meat  industry  is  one 
of  the  most  important  enter- 
prises in  our  country.     In  a 
recent  year  the  production  of 
beef,  veal,  mutton  and  pork 
amounted    to    22,378,000,000 
lb.,  an  average  of  about  220 
lb.    for   each    person   in    the 
United    States.      Not    all    of 
this  immense  production  of  meat  was  consumed  in  this  country, 
however,  for  a  large  portion  of  it  was  exported  to  foreign 
countries. 

Exercise  17 

1.  A  farmer  sold  a  carload  of  20  steers  averaging  1250  lb. 
in  weight  for  $11.00  per  hundred  pounds.  How  much  did  he 
receive  for  them? 

2.  If  one  of  these  steers  loses  40%  in  being  dressed,  what 
is  the  weight  of  the  dressed  beef  in  a  steer  weighing  1250  lb.? 

3.  If  a  steer  weighing  1093  pounds  alive  weighs  632  pounds 
when  dressed,  what  per  cent  did  this  steer  lose  in  being  slaugh- 
tered? 

4.  The  two  loins  of  a  hog  weigh  about  10%  of  the  weight  of 
a  live  hog.  How  much  would  each  of  the  loins  from  a  220- 
Ib.  hog  weigh? 

5.  A  farmer  ships  a  carload  of  95  hogs  averaging  225  pounds 
in  weight,  receiving  $12.35  per  hundred.  How  much  did  he 
receive  for  the  carload  of  hogs? 

6.  Find  the  broker's  commission  at  $10.00  per  carload  of 
19,000  lb.  and  5  cents  per  hundred  in  excess  of  that  weight. 


PERCENTAGE— THE  MEAT  INDUSTRY 


79 


In  slaughtering  a  beef,  the  waste  materials  are  all  used. 
From  these  waste  materials  or  by-products  are  made  leather, 
glue,  oleo  oil,  soap  and  fertilizers. 

The  carcass  of  a  beef  is  divided 
into  8  different  cuts  as  shown  in 
the  illustration  at  the  left.  The 
percentage  of  the  dressed  weight 
included  in  each  cut  of  the  beef  is 
also  shown. 


1  Hound  24. 

2  Loin  16.60- 
SJFJank  2.53  - 
4  Rib  9,64  • 
SJVavet  8.46  ■ 
6£rishee  6.00' 
7CItucA  22.06 
SjShank  6. 7 J 
9-^uef     ■    3.98 


loo.^ 


7.  A  dressed  carcass  of  a  steer 
weighs  670  lb.  Find  the  weight 
included  in  each  of  the  different 
cuts  for  one-half  of  the  carcass, 
using  the  percentages  in  the  illus- 
tration. 

8.  If  the  by-products  of  a  steer  costing  $132  were  estimated 
as  worth  $36,  what  per  cent  of  the  original  cost  of  the  steer 
was  obtained  from  the  by-products? 

9.  A  hog  loses  25%  to  35%  of  its  weight  in  being  dressed. 
How  much  will  a  200-lb.  hog  lose  in  weight  if  the  loss  is  33%? 

10.  How  much  will  the  200-lb.  hog  weigh  when  dressed? 

11.  How  much  will  a  175-lb.  hog  weigh,  dressed;  shrinking 
35%? 

12.  The  two  short  cut  hams  of  a  hog  are  about  13  f%  of 
the  live  weight  of  a  hog.  How  much  do  the  two  short  cut 
hams  of  a  230-lb.  hog  weigh? 

Oleomargarine  is  one  of  the  most  important  products  made 
by  the  packing  industry.  It  is  made  from  a  mixture  of  oleo 
oil,  neutral,  vegetable  oil,  milk  and  cream,  and  butter.  The 
oleo  oil  is  made  from  the  fat  of  cattle.  Neutral  is  made  from 
the  finest  leaf  fat  of  hogs.  The  vegetable  oils  include  such  oils 
as  cottonseed  oil  and  peanut  oil. 


80  SEVENTH  YEAR 

13.  The  wholesale  price  on  a  certain  brand  of  oleomargarine 
was  24j!f  per  pound  in  December  of  a  recent  year.  The  cheapest 
brand  made  by  the  same  firm  was  selling  at  only  75%  of  that 
price.     What  was  the  price  of  the  cheaper  grade? 

14.  The  retail  price  of  the  best  brand  of  oleomargarine 
mentioned  in  problem  13  was  28^  at  a  certain  grocery  store. 
The  retail  price  was  how  many  per  cent  greater  than  the  whole- 
sale price? 

15.  A  certain  meat  packing  firm  states  that  80%  of  their 
sales  go  for  the  purchase  of  live  stock,  8%  for  labor,  5%  fo; 
freight  and  4f  %  for  other  expenses.  What  per  cent  of  their 
sales  is  left  for  dividends  for  the  stockholders? 

16.  If  their  total  sales  amounted  to  $500,000,000  per  year, 
compute  the  amount  paid  for  live  stock,  the  amount  paid  for 
labor  and  the  amount  left  for  dividends. 

The  receipts  at  the  nine  principal  live  stock  markets  in  the 
United  States  for  the  years  ending  October  1  are  as  follows: 

Cattle  Sheep  Hogs 

1911 9,416,374  13,530,833  19,217,506 

1912 8,861,404  14,148,096  21,035,035 

1913 9,188,500  14,146,284  19,997,656 

1914 8,193,856  14,702,889  19,366,263 

1915 8,464,185  11,994,851  21,366,263 

17.  What  has  been  the  percent  of  decrease  in  the  number 
of  cattle  from  1911  to  1915? 

18.  What  has  been  the  per  cent  of  decrease  in  the  number 
of  sheep  received  from  1914  to  1915? 

19.  What  was  the  per  cent  of  increase  in  the  supply  of  hogs 
from  1911  to  1915? 

20.  The  average  wholesale  price  of  dressed  beef  in  New  York 
in  1911  was  $8.77  and  in  1915  it  was  $11.64.  What  has  been 
the  per  cent  of  increase  in  the  wholesale  price  of  beef  in  that 
period? 


PERCENTAGE— THE  COTTON  INDUSTRY   81 


COTTON 


When  picked,  cotton  is 
first  ginned/  and  then 
packed  into  bales  weighing 
approximately  500  pounds. 
To  economize  space  in  ship- 
ping long  distances  these 
bales  usually  are  com- 
pressed by  powerful  ma- 
chines into  the  smallest 
possible  compass.      The 

illustration     shows    one     of  High  Density  Cotton  Compress 

these  machines  compressing   a  bale  of  cotton. 

The  following  table  gives  the  number  of  bales  produced  in 
the  leading  cotton-producing  states. 


No.  of  bales 
1913 

Texas 3,945,000 

Georgia , 2,317,000 

South  Carolina 1,378,000 

Alabama 1,495,000 

Mississippi 1,311,000 

Arkansas 1,073,000 

North  Carolina 793,000 


Oklahoma 

Louisiana 

Tennessee 

Missouri 

Florida 

Virginia 

All  other  states. 


840,000 
444,000 
379,000 
67,000 
59,000 
23,000 
32,000 


'  United  States 14,156,000 


No.  of  bales 

1914 

4,592,000 

2,718,000 

1,534,000 

1,751,000 

1,246,000 

1,016,000 

931,000 

1,262,000 

449,000 

384,000 

82,000 

81,000 

25,000 

64,000 

16,135,000 


No.  of  bales 

1915 

3,175,000 

1,900,000 

1,160,000 

1,050,000 

940,000 

785,000 

708,000 

630,000 

360,000 

295,000 

62,000 

60,000 

16,000 

40,000 

11,161,000 


Total  Value  of  Crop .  $885,350,000  $591,030,000  $602,393,000 

'Ginning  is  the  process  of  removing  the  seeds  from  the  cotton. 


82  SEVENTH  YEAR 

Exercise  18 

1.  What  was  the  per  cent  of  increase  in  the  number  of  bales 
of  cotton  from  1913  to  1914?     (See  preceding  page.) 

2.  Find  the  price  per  pound  for  cotton  in  1913;  for  1914  and 
for  1915.  The  large  crop  and  the  outbreak  of  the  great  European 
War  in  1914  were  responsible  for  the  low  price  in  1914.  Com- 
pute the  prices  per  bale. 

3.  Note  the  decreased  production  in  1915.  What  was  the 
per  cent  of  decrease  from  the  yield  for  1914? 

4.  Wnat  per  cent  of  the  total  production  of  the  United 
States  was  the  production  of  Texas  in  1914;  in  1915? 

5.  The  production  of  Oklahoma  in  1915  was  what  per  cent 
of  its  production  in  1914? 

6.  The  total  production  of  the  United  States  for  1914  was 
what  per  cent  greater  than  the  total  production  for  1915? 

7.  The  total  exports  of  cotton  for  1913  was  4,562,295,675 
lb.  What  was  the  value  of  our  cotton  exports  in  1913  at  12.2 
cents  per  pound? 

8.  Cotton  constitutes  about  53%  of  our  total  agricultural 
exports.  From  the  data  given  in  problem  7,  compute  the  value 
of  our  total  agricultural  exports  for  1913. 

9.  It  is  estimated  that  cotton  forms  63%  of  the  total  crop 
production  in  Texas.  From  the  data  in  the  table  and  the  cost 
per  pound  in  problem  2,  find  the  value  of  the  total  crop  pro- 
duction of  Texas  in  1915. 

This  offers  a  valuable  type  of  work — getting  information  from  a  table 
of  statistics.  Additional  exercises  of  this  type  may  be  made  from  tables 
of  statistics  such  as  those  found  in  the  Statesman's  Year  Book  or  other 
similar  publications.     Make  similar  comparisons  with  repent  data. 


PERCENTAGE— FOOD  PRICES 


83 


Exercise  19 

The  following  table  shows  the  increases  in  wholesale  prices 
of  some  of  the  most  important  food  products : 


1915  Prices     1920  Prices 


%of 

Increase 

? 


Food  Product 

Hams,  fresh $    .16  $     .30 

Bacon 24 46 ? 

Beef,  No.  1  ribs 17 35  ... .  ? 

Chickens,  broilers 20^ 53   ? 

Eggs,  No.  1 24§ 4U....  ? 

Potatoes,  bushel 48  4.50 ? 

Corn,  small  cans,  per  doz 78  1.25   ...  .  ? 

Navy  beans,  bushel 3.15   5.25   ....  ? 

Apples,  barrel 3.25   10.50 ? 

Flour,  barrel 6.25   15.50  ....  ? 

Sugar,  gran.,  per  100  lbs 5.50  21.00 ? 

Rolled  oats,  pound 03 06  ? 

1.  Find  the  per  cent  of  increase  for  each  food  product  given 
in  the  table. 

2.  Find  the  average  per  cent  of  increase  in  all  of  these  food 
products. 

3.  Ascertain  if  possible  the  present  wholesale  prices  on  the 
food  products  hsted  in  the  table  and  determine  the  per  cents 
of  increase  or  decrease  from  the  prices  in  the  record  column. 

4.  From  the  market  reports  in  today's  paper  get  the  prices 
of  com,  oats,  hogs,  cattle,  cotton,  rice,  wheat,  eggs,  butter,  hay, 
potatoes,  oranges,  apples  and  other  farm  products  in  which  you 
are  interested.  From  a  last  year's  paper  of  about  the  same 
time  of  the  year,  get  the  prices  of  the  same  products.  Compute 
the  per  cents  of  increase  or  decrease  for  the  last  year. 

5.  Secure  at  a  local  grocery  store  the  retail  prices  on  a  list 
of  at  least  10  food  products  for  this  year  and  also  the  prices  for 
last  year  on  the  same  quality  of  goods.  Find  the  per  cent  of 
increase  or  decrease  on  each  of  the  articles  that  you  have  listed. 
Ask  the  grocer  to  tell  you  the  causes  for  the  increases  or  de- 
creases on  the  various  articles. 


84  SEVENTH  YEAR 

FOOD  VALUES 

There    are   four    principal    food 
substances  in  the  foods  that  we  eat: 
(1)    protein   (pro'-te-in)    (2)   carbo- 
73.7  %     hydrate;  (3)  fat;  (4)  mineral  matter. 
"WKTTR      Water  is  also  an  important  con- 
^         stituent  of  food  products.     Differ- 
'pROTEIN       ^^*  ^^^^  products  contain  different 
''lO.S  %  FAT      proportions  of  these  food  substances. 
^^/  Ash  Eggs,  as  shown  in  the  illustration, 

are    composed    of    73.7%    water, 
14.8%  protein,  10.5%  fat  and  1%  ash  or  mineral  matter. 

The  protein  compounds  not  only  build  up  the  tissues  of  the 
body  but  they  also  furnish  energy  to  enable  us  to  do  our  work. 
The  carbohydrates  and  fats  supply  energy  for  the  body. 

Exercise  20 

1.  Using  the  percentages  given  in  the  illustration  above, 
find  the  number  of  ounces  of  each  of  the  constituents  in  a  pound 
of  eggs. 

2.  The  average  composition  of  1  pound  of  beef  is  as  follows: 
water  10.72  oz.;  protein  3.04  oz.;  fat  2.08  oz.;  and  mineral 
matter  .16  oz.  Find  the  per  cent  of  each  substance  in  the 
average  pound  of  beef. 

3.  A  white  potato  is  composed  of  1.8%  protein,  .1%  fat, 
14.7%  carbohydrates,  .8%  ash,  62.6%  water  and  20%  refuse. 
Find  the  number  of  ounces  of  each  constituent  in  1  lb.  of  pota- 
toes.    (Refer  to  page  312  for  additional  data  for  problems.) 

4.  White  bread  is  composed  of  9.2%  protein,  1.3%  fat, 
53.1%  carbohydrates,  1.1%  ash,  35.3%  water.  How  many 
ounces  are  there  of  each  food  substance  in  a  pound  loaf  of  bread? 

6.  Compare  amounts  of  various  food  substances  in  bread 
and  potatoes. 


PERCENTAGE  PROBLEMS— FOOD  VALUES   85 

6.  If  cereals  and  their  products  supply  62%  of  the  carbo- 
hydrates, and  vegetables  and  fruits  together  16%  of  the 
carbohydrates,  what  per  cent  of  the  total  carbohydrates  do 
both  of  these  classes  supply? 

7.  If  meat  and  poultry  supply  16%  of  the  total  food  material 
in  the  average  American  home,  and  dairy  products  18%, 
cereals  and  their  products  31%,  vegetables  and  fruits,  together, 
25%,  how  much  of  the  total  food  materials  do  these  items 
constitute? 

8.  If  meat  and  poultry  supply  30%  of  the  protein,  the 
dairy  products  10%  of  it,  cereals  and  their  products  43%  of  it, 
and  vegetables  and  fruits  together  9%  of  it,  how  much  of  the 
protein  is  suppUed  by  these  four  kinds  of  food? 

9.  If  meat  and  poultry  supply  59%  of  the  fat,  dairy  prod- 
ucts 26%  of  the  fat,  cereals  and  their  products  9%  of  the 
fat,  and  fruits  and  vegetables  together  2%  of  the  fat,  what 
per  cent  of  the  total  fat  do  these  four  kinds  of  food  supply? 

Domestic  science  courses  not  only  teach  how  to  cook  foods 
but  also  what  kinds  of  foods  to  prepare  in  order  to  secure  a 
proper  proportion  of  the  various  food  substances.  When  coal 
is  burned,  it  supplies  heat  which  may  be  converted  into  the 
energy  of  steam  and  run  a  steam  engine.  In  a  similar  manner 
the  food  which  we  eat  is  consumed  by  our  bodies,  supplying 
heat  and  energy  to  do  our  work.  Experiments  have  been  made 
to  show  the  amount  of  energy  which  each  food  product  yields. 
These  amounts  of  energy  are  expressed  in  terms  of  calories 
(kal'-o-ries). 

A  calorie  is  used  in  this  connection  to  mean  the  amount  of 
heat  required  to  raise  1  pound  of  water  4°  Fahrenheit. 

The  number  of  calories  per  day  needed  by  any  person  varies 
with  his  weight  and  the  amount  of  work  which  he  does.  A 
man  at  hard  work  or  an  active  growing  boy  may  require  as 


86  .  SEVENTH  YEAR 

much  as  5000  calories  of  food  energy  per  day.  An  average  man 
requires  about  2500  calories  when  engaged  in  an  occupation 
where  he  is  sitting  most  of  the  day. 

The  problem  of  the  scientific  cook  is  to  serve  foods  which 
will  contain  the  proper  food  substances  and  at  the  same  time 
supply  a  sufficient  number  of  calories  each  day. 

The  following  table^  shows  the  amount  of  each  food  product 
which  will  yield  100  calories: 

Milk f  cup,  whole;  l|^  cups,  skim 

Cream J  cup,  thin;  1^  tablespoons,  very  thick 

Butter 1  tablespoon 

Bread 2  slices  3"x3|"x|" 

Fresh  fruit 1  large  orange  or  apple 

Eggs 1  large,  1^  medium 

Meat  (beef,  mutton,  chicken,  etc.) About  2  oz.  lean 

Bacon  (cooked  crisp) About  f  oz.  (very  variable) 

Potatoes 1  medium 

Sugar 1  tablespoon 

Cocoa,  made  with  milk %  oi  a,  cup 

Cooked  or  flaked  breakfast  foods f  to  Ij  cups 

Dried  fruit 4  or  5  prunes  or  dates 

Exercise  21 

1.  A  man  requiring  2500  calories  per  day  eats  the  following 
breakfast:  1  cup  of  breakfast  food  with  ^  cup  of  thin  cream, 
1  cup  of  cocoa  made  with  mulk,  2  slices  of  bread,  1  tablespoon 
of  butter,  2  small  slices  of  bacon  and  1  egg  (large).  Find  the 
number  of  calories  supplied  by  this  breakfast. 

2.  What  per  cent  of  the  total  requirement  for  a  day  is 
furnished  by  that  breakfast? 

3.  It  is  desirable  that  a  family  of  five  consume  3  quarts 
of  milk  per  day.  If  they  consume  17  quarts  per  week,  what 
per  cent  of  the  desirable  quantity  have  they  used? 

'See  Rose,  Feeding  the  Family. 


PERCENTAGE  PROBLEMS— FOOD  VALUES   87 

4.  From  the  preceding  table,  prepare  a  menu  for  breakfast 
that  will  furnish  between  700  and  900  calories. 

5.  Prepare  a  menu  for  lunch  to  furnish   approximately 
1000  calories. 

6.  Which  will  furnish  the  largest  number  of  calories,   a 
large  orange  or  a  medium  sized  egg?     (See  table,  page  86.) 

7.  How  many  calories  will   a  dozen  medium  sized  eggs 
supply? 

8.  How  many  calories  are  there  in  a  quart  of  milk?  (2  cups 
make  a  pint.) 

9.  How  many  calories  are  there  in  a  pound  of  prunes  (40 
to  the  pound)? 

10.  A  man  requiring  3000  calories  per  day  eats  a  breakfast 
furnishing  700  calories,  a  lunch  furnishing  about  900  calories 
and  a  dinner  furnishing  about  1400  calories.  Find  the  per 
cent  of  the  total  furnished  by  each  meal. 

11.  If  the  meals  for  a  family  for  a  week  cost  $5.60  and  the 
meat  costs  $1.40,  the  vegetables  70  cents  and  the  butter  48 
cents,  what  per  cent  of  the  total  was  spent  for  each  group? 

12.  What  per  cent  of  the  weekly  expense  was  left  for  other 
materials? 

13.  If  it  takes  1  hour  to  prepare  an  entire  meal  and  20  min- 
utes to  make  the  dessert,  what  per  cent  of  the  whole  time  is 
given  to  the  dessert? 

The  following  table  shows  the  number  of  calories  supplied 
by  a  pound  of  each  food  product: 

Beef,  fresh  lean 709  Beans 1564 

Beef,  fat 1357  Oatmeal 1810 

Bacon  (average) 2836  Lettuce 87 

Butter 3488  Cabbage 143 

Apples 285  Sugar 1814 

Potatoes,  white 378  Bread 1174 

Milk,  whole 314  Eggs 672 


88  SEVENTH  YEAR 

Exercise  22 

1.  The  food  value  of  a  pound  of  fresh  lean  beef  is  what  per 
cent  of  the  food  value  of  a  pound  of  butter? 

2.  A  pound  of  white  potatoes  furnishes  what  per  cent  as 
many  calories  as  a  pound  of  butter? 

3.  How  does  the  food  value  of  a  pound  of  lettuce  compare 
with  the  food  value  of  a  pound  of  white  potatoes?  (Express  in 
per  cent.) 

4.  In  the  same  way  compare  the  food  values  ol  fat  beef 
and  bacon. 

6.  Which  is  cheaper,  sugar  at  11  cents  per  pound  or  beans 
at  12  cents  per  pound,  considering  the  food  values  of  each? 

6.  Which  is  cheaper,  apples  at  10  cents  per  pound  or  bacon 
at  35  cents  per  pound? 

7.  Which  is  cheaper,  oatmeal  at  8  cents  per  pound  or  eggs 
at  35  cents  per  dozen?     (Figure  eggs  at  1^  lb.  per  doz.) 

8.  From  the  cost  of  milk  and  butter  in  your  community, 
compute  the  cost  of  the  amount  of  each  necessary  to  supply 
100  calories. 

9.  Find  the  cost  of  100  calorie  portions  of  cabbage,  potatoes, 
lean  beef,  beans,  sugar,  bread,  eggs  and  bacon  in  your  commu- 
nity. 

10.  Prepare  a  menu  for  a  lunch  from  the  items  listed  on  page 
75,  providing  900  calories  for  each  of  4  persons.  From  local 
prices  in  your  community,  estimate  the  cost  of  this  lunch  for 
each  person. 

11.  Prepare  and  present  a  problem  on  food  values  to  the 
class  for  solution. 

12.  If  you  have  a  school  lunch  room,  estimate  the  cost  to 
the  students  of  100  calorie  portions  of  as  many  of  the  dishes 
as  you  can  find  the  data  to  compute. 


CHAPTER  IV 
APPLICATIONS  OF  PERCENTAGE 

The  subjects  treated  in  this  chapter  do  not  involve  any  new 
principles  of  percentage  but  merely  an  application  of  the  prin- 
ciples already  mastered  to  new  business  situations.  New 
terms  and  new  business  forms  will  have  to  be  mastered  in 
making  the  application  of  the  principles  already  learned. 
The  discussion,  then,  at  the  beginning  of  each  list  of  problems 
should  be  thoroughly  mastered  in  order  to  get  a  good  knowledge 
of  business  terms  and  organization. 

BUSINESS  TRANSACTIONS 

Exercise  1 

The  gross  profit  in  any  business  transaction  is  the  difference 
between  the  cost  price  and  the  selling  price.  The  net  profit 
is  the  gross  profit  less  the  expenses  of  the  transaction. 

1.  A  notion  store  sold  100  pairs  of  wooden  knitting  needles 
at  10  cents  per  pair,  at  a  profit  of  33|%.  What  was  the  cost 
of  each  pair  of  needles? 

2.  If  the  selling  price  of  an  article  is  4  times  the  cost,  what 
is  the  per  cent  of  gain? 

3.  A  fancy  vest  is  sold  for  $7  at  a  profit  of  40%.  What 
was  its  cost  price? 

4.  A  village  lot  was  purchased  for  $1000,  but  because  of  a 
decline  in  real  estate  values  was  sold  for  $750.  What  was  the 
per  cent  of  loss? 

5.  A  man  sold  a  horse  for  $120  at  a  loss  of  25%.  What 
did  the  horse  cost  him? 

89 


90  SEVENTH  YEAR 

6.  A  merchant  bought  goods  listed  at  $1200  at  a  reduction 
of  40%.  He  sold  them  at  a  profit  of  25%.  What  was  the  total 
selling  price  of  the  goods? 

7.  A  merchant  having  goods  worth  $10,000  increased  his 
stock  25%  and  sold  the  entire  stock  at  an  average  profit  of 
20%.    For  what  sum  did  he  sell  it? 

8.  When  an  article  that  cost  $24  is  sold  at  a  profit  of  10% 
and  the  purchaser  sells  it  again  at  a  loss  of  20%,  what  is  its 
last  selHng  price? 

9.  A  liveryman  sold  a  horse  for  $175  at  a  profit  of  25%. 
What  was  the  cost  of  the  horse? 

10.  A  man  sold  two  farms  for  $7500  each.  On  one  he  gained 
20%  and  on  the  other  he  lost  20%.  Did  he  gain  or  lose  on  the 
entire  transaction  and  how  much? 

11.  A  farmer  bought  a  herd  of  20  steers,  averaging  1100 
lb.  each,  at  $7.50  per  hundred.  He  fed  them  700  bu.  of  corn 
worth  65^  per  bu.,  15  tons  of  hay  worth  $12  per  ton  and 
roughage  worth  $60.  If  his  pasture  of  20  acres  was  worth  $6 
per  acre,  what  was  his  profit  on  the  herd  of  cattle  if  they  weighed 
1475  lb.  and  brought  $10.50  per  hundred  when  he  sold  them? 

12.  A  farmer  sold  his  neighbor  a  cow  at  an  advance  of  10% 
of  what  she  cost  him.  His  neighbor  sold  her  to  a  dairyman  at 
an  advance  of  25%,  receiving  $110  for  the  cow.  Find  the 
amount  of  profit  made  by  each. 

13.  A  manufacturer  sold  a  hardware  dealer  a  stove  at  a 
profit  of  10%  on  the  cost  of  manufacturing.  The  hardware 
dealer  sold  the  stove  to  a  customer  for  $61.60  at  a  profit  of 
40%.    Find  the  cost  to  the  manufacturer. 

14.  A  dairyman  sold  two  cows  for  $90  each.  On  one  he 
gained  20%  and  on  the  other  he  lost  10%.  Find  his  per  cent 
of  gain  or  loss  on  the  entire  transaction. 


APPLICATIONS  OF  PERCENTAGE— DISCOUNTS  91 

DISCOUNTS 
Exercise  2 

A  discount  is  a  sum  deducted  from  the  price  of  an  article. 
Discounts  are  usually  computed  by  per  cents.  To  state  that 
you  will  sell  an  article  at  a  discount  of  25%  means  that  you 
will  sell  it  for  j  off  or  25%  off  the  regular  list  price. 

Many  firms  give  discounts  for  cash  purchases.  It  is  profitable 
for  these  firms  to  give  small  discounts  for  cash  purchases 
because  they  can  re-invest  the  money  and  be  making  additional 
profits. 

1.  A  music  dealer  sold  a  piano  which  he  had  listed  for  $400 
at  a  discount  of  20%.    How  much  did  he  receive  for  it? 

List  price  of  the  piano  =  $400 

20%  of  $400  =  i  of  $400  = 80  =  the  discount. 

He  received $320 

The  amount  that  is  left  after  the  discount  is  subtracted  from 
the  list  price  is  called  the  net  proceeds.  In  problem  1,  $400  is 
the  list  price,  $80  is  the  discount  and  $320  is  the  net  proceeds. 

Find  the  discounts  and  net  proceeds  of  the  following  list 
prices  at  the  stated  discounts: 

2.  $100,  25%.  6.  $1.00,  30%.  10.  $20,         15%. 

3.  $  25,  10%.  7.  $1.50,  33 J%.  11.  $40,         25%. 

4.  $250,  20%.  8.  $500,     2%.  12.  $5.00,      10%. 

5.  $  30,  40%.  9.  $125,  20%.  13.  $452.75,    2%. 

14.  After  using  a  motorcycle,  costing  $150,  for  a  month, 
a  boy  offered  it  for  sale  at  a  discount  of  15%  of  the  cost  price. 
How  much  did  he  want  for  the  motorcycle? 

16.  A  merchant  bought  a  bill  of  goods  amounting  to  $1240 
and  received  a  cash  discount  of  2%  for  prompt  payment.  What 
was  the  net  proceeds  of  his  bill? 


92  SEVENTH  YEAR 

CLEARANCE  SALES 

Exercise  3 

Retail  stores  have  clearance  sales  in  order  to  dispose  of  old 
goods  on  hand  and  make  room  for  new  styles  and  up-to-date 
patterns.  They  often  give  reductions  of  10%,  20%,  33|%,  or 
even  as  high  as  50%.  In  order  to  dispose  of  goods  left  on 
hand  in  which  the  styles  are  likely  to  change,  the  merchant 
may  offer  the  goods  at  cost  in  order  to  prevent  a  loss  at  a  later 
date  when  the  goods  are  out  of  style. 

1.  A  merchant  advertised  a  20%  discount  sale  on  shirts. 
How  much  was  the  price  on  a  shirt  listed  regularly  at  $2.50? 

2.  A  clothier  offers  a  discount  of  15%  on  all  suits  and  over- 
coats in  his  store.    What  is  his  sale  price  on  suits  listed  at  $25? 

3.  A  furniture  store  advertised  a  closing  out  sale,  offering 
a  discount  of  33^%  on  the  regular  prices.  Find  the  cost  of 
the  following  articles  listed  regularly  as  follows:  1  library 
table — $30.00;  2  rocking  chairs  at  $15.00  each;  1  davenport — 
$42.00;  1  brass  bed— $24.00;  1  mattress— $12.00;  1  set  of 
springs— $9.00;  and  1  dresser— $24.00. 

4.  In  a  clearance  sale,  a  merchant  gave  a  discount  of 
40%  on  novelty  dress  goods  and  20%  on  the  staple  weaves. 
Why  could  he  afford  to  give  a  larger  discount  on  the  novelty 
goods? 

6.  One  shoe  store  advertised  a  ceitain  shoe  that  retails 
regularly  at  $4.00  for  $3.45;  another  store  advertised  the  same 
shoe  at  a  discount  of  15%.  Which  was  the  better  offer  and  how 
much? 

6.  A  merchant  advertised  $2.00  silks  at  a  discount  of  20%. 
What  was  his  sale  price  on  those  silks? 

7.  Straw  hats  worth  $3.00  early  in  the  season  were  sold 
late  in  the  season  at  $1.50.    What  was  the  per  cent  of  discount? 


APPLICATIONS  OF  PERCENTAGE— DISCOUNTS  93 

COMMERCIAL  DISCOUNTS 

Exercise  4 

Wholesale  dealers  and  manufacturers  often  offer  two  or 
more  discounts  off  the  list  price.  These  discounts  axe  called 
trade  or  commercial  discounts. 

There  are  several  advantages  in  using  this  system  of  com- 
mercial discounts.  In  the  first  place,  catalogues  are  expensive 
to  issue.  By  making  the  list  prices  of  the  articles  high,  fluctua- 
tions in  the  cost  of  materials  will  not  make  it  necessary  to  issue 
a  new  catalogue.  Instead,  the  firm  can  merely  send  out  a 
new  discount  sheet  which  gives  the  discounts  allowed  on  the 
various  classes  of  articles.  This  discount  sheet  costs  very 
little  compared  with  the  original  cost  of  the  catalogue.  Further- 
more a  retail  dealer  can  show  his  customer  the  catalogue  and 
give  him  a  discount  on  the  list  price  without  the  customer 
knowing  the  extent  of  his  profit.  Can  you  think  of  any  other 
advantages  of  commercial  discounts? 

If  a  firm  is  selling  goods  at  a  certain  discount,  a  decrease  in  the  cost  of 
production  may  enable  them  to  add  a  second  discount.  A  discount  is 
also  usually  allowed  for  prompt  payment.  Consequently,  we  occasionally 
see  goods  listed  subject  to  a  series  of  three  successive  discounts. 

Commercial  discounts  are  computed  in  sucession.  The 
first  discount  is  taken  from  the  list  price  and  the  second  dis- 
count is  then  computed  on  the  remainder  and  so  on. 

1.  A  bed  room  suite  was  listed  at  $80  less  discounts  of  20% 
and  10%.    What  was  the  net  price? 

20%X$80    =$16,  the  first  discount. 
$80  —$16    =$64,  the  remainder. 
10%  X  $64    =  $6.40,  the  second  discount. 
$64  -$6.40  =  $57.60,  the  net  price. 
The  net  price  is  the  list  price  less  the  conmiercial  discounts. 


U  SEVENTH  YEAR 

2.  A  piano  listed  at  $500  has  discounts  of  30%  and  5%. 
Find  the  net  price. 

8.  A  hardware  firm  quotes  a  certain  grade  of  hammers  at 
$12  a  dozen,  less  discounts  of  33^%  and  25%.  What  is  the 
cost  of  each  hammer  to  a  local  dealer?  What  must  he  mark 
a  hammer  to  make  a  profit  of  50%? 

4.  A  merchant  buys  sweaters  from  a  factory  at  $24 
per  dozen  at  discounts  of  20%  and  5%.  What  must  he  sell 
them  at  in  order  to  make  a  profit  of  60%? 

6.  Stoves  are  quoted  by  a  manufacturer  at  $40  each,  subject 
to  discounts  of  25%,  10%  and  5%.  What  is  the  net  price  to 
the  retail  dealer  if  he  is  allowed  a  further  discount  of  2%  for 
cash? 

6.  Find  the  net  price  on  a  dining  table  and  set  of  six  chairs 
listed  at  $80  if  discounts  of  20%  and  15%  are  allowed. 

7.  A  music  cabinet  is  listed  at  $65  with  discounts  of  25%, 
10%  and  5%.    Find  the  net  price. 

List  price  Discount  Net  price 

8.  $175  20%,  10%  and  5%  ? 

9.  $150  25%  and  5%  ? 

10.  $400  30%,  10%  and  5%  ? 

11.  $40   ■  20%  and  3%,  ? 

12.  $75  25%,  and  2%  ? 

In  order  to  save  computation,  firms  have  tables  showing 
a  single  discount  which  is  equivalent  to  the  series  of  successive 
discounts. 

13.  What  single  discount  is  equivalent  to  successive  discounts 
of  20%  and  10%? 

20%  X 100%  =  20%  10%  X  80%  =  8% 

100%-  20%  =  80%  80%-     8%  =  72%,  net  price. 


APPLICATIONS  OF  PERCENTAGE— DISCOUNTS  95 

100% -72%  =  28%. 

Therefore,  28%  is  equivalent  to  successive  discounts  of  20% 
and  10%. 

14.  What  single  discount  is  equivalent  to  successive  discounts 
of  30%  and  20%? 

15.  Find  the  single  discount  equivalent  to  commercial  dis- 
counts of  25%),  10%  and  5%. 

16.  Which  is  better,  a  single  discount  of  40%  or  successive 
discounts  of  25%  and  20%?    How  much  better? 

17.  Find  the  net  price  of  a  bill  of  goods  amounting  to  $280 
with  discounts  of  25%  and  10%  with  an  additional  discount 
of  2%  for  cash. 

18.  Find  the  net  price  on  a  set  of  harness  listed  at  $60, 
subject  to  discounts  of  20%  and  10%. 

Note:    Bank  Discount  will  be  treated  under  the  topic  Banks. 

INTEREST 

Exercise  5 

Much  of  the  business  of  the  world  is  carried  on  with  borrowed 
money.  Men  of  ability  and  industry  often  do  not  have  enough 
money  of  their  own  to  supply  the  capital  necessary  for  estab- 
lishing or  conducting  their  business  enterprises.  On  the 
other  hand  there  are  men  who  prefer  to  loan  their  money  rather 
than  attempt  to  run  a  business  of  their  own. 

Thus  money  is  loaned,  in  the  business  world,  not  as  a  matter 
of  personal  favor  or  accommodation,  but  as  a  matter  of  busi- 
ness based  on  benefits  to  both  lender  and  borrower.  The 
person  who  lends  the  money  receives  pay  for  the  use  of  it  from 
the  borrower.  Money  paid  for  the  us^  of  money  is  called 
interest. 


96  SEVENTH  YEAR 

The  borrower  in  receiving  money  loaned  to  him,  gives  a 
dated  and  signed  promise  to  return  the  money  loaned  (or  the 
principal)  with  a  certain  interest  at  a  stated  date.  Such  a 
paper  is  called  a  note.    Here  is  a  note  of  simple  form: 


§1500.00 ,......£)dly?y^ufE^:ip^y^  

J^J>^^A4^_£)g/UAi.,.     afur  date  , Cf. promise  to  pay  to 

,..M^,.&.OC_or  order  QmMm^^?^ 


with  interest  at  .V../?/. fir  value  received. 

f^MJia/uL^^ifO 


In  a  new  community,  where  capital  is  greatly  needed,  money 
would  often  command  a  much  higher  rate  of  interest  than  the 
law  would  allow.  Most  states  provide  penalties  for  charging 
a  higher  rate  of  interest  than  the  legal  rate  fixed  by  law.  The 
laws  of  the  different  states  are  not  uniform  as  to  the  rate  of 
interest  that  will  be  permitted.  Interest  that  is  unlawful  in 
rate  is  called  usury.  Find  what  is  the  legal  rate  of  interest  in 
your  state  by  inquiring  at  the  bank. 

In  ordinary  transactions  involving  interest  any  month  is 
considered  one-twelfth  of  the  year  and  thirty  days  constitute 
a  month.  In  the  case  of  large  amounts  of  money,  where 
exactness  as  to  time  is  very  important,  the  time  of  the  loan  is 
often  stated  in  days  and  is  reckoned  according  to  agreement  or 
custom.    In  exact  interest  365  days  are  considered  a  year. 

Since  banks  consider  360  days  a  year  in  computing  bank 
discount,  it  is  customary  to  figure  interest  on  that  basis.  The 
following  form  is  very  convenient  for  computing  simple  interest 
because  it  allows  one  to  use  cancellation: 


APPLICATIONS   OF   PERCENTAGE— INTEREST  97 

Find  the  interest  on  $300  for  1  year,  3  months  and  15  days  at 
6%. 

3  93 

$300X-|,X^  =  ?p  =  $23.25. 
Z00    360      4 

00 

20 

4 

In  the  above  problem,  the  rate  is  used  as  a  common  fraction 
YQ-Q ;  the  time  1  year  (360  days) +3  months  (90  days) +  15  days 
=465  days  which  is  ^^  of  a  year.  The  interest  for  1  year 
($300  XxQ^)  must  therefore  be  multiplied  by  l-ff  to  find  the 
interest  for  the  given  time. 

When  the  time  is  expressed  in  years  and  months,  the  form 
can  be  shortened  by  expressing  the  years  and  months  as  twelfths 
of  a  year. 

Find  the  interest  on  $200  for  1  year,  6  months  at  6%. 

^        0       18 

^20^Xz00xrr^''- 

2 
Find  the  interest  on: 

1.  $500  for  6  months  at  6%. 

2.  $350  for  1  year  at  7%. 

3.  $1000  for  2  years  at  6%. 

4.  $2000  for  2  years  at  5  J%. 

5.  $250  for  2  years,  6  months  at  7%. 

6.  $6500  for  5  years,  6  months  at  5%. 

7.  $325  for  2  years,  9  months  at  6%. 

8.  $480  for  1  year,  8  months,  15  days  at  6%. 


98  SEVENTH  YEAR 

9.  $2000  for  2  years,  8  months,  20  days  at  5%. 

10.  $500  for  1  year,  5  months,  18  days  at  6%. 

11.  $425.50  for  1  year,  3  months,  21  days  at  6%. 

12.  $218.50  for  2  years,  10  months,  12  days  at  6%. 

13.  $350.75  for  2  years,  8  months,  19  days  at  6%. 

14.  $875.25  for  1  year,  3  months,  27  days  at  6%. 

16.  $5000  for  4  years,  7  months,  18  days  at  5%. 
^  $150  for  1  year,  3  months,  20  days  at  7%. 

17.  $200  for  6  months  at  3%. 

18.  $175  for  1  year,  2  months,  15  days  at  6%.  ;/ 

19.  $300  for  2  years,  4  months  at  6%.  '^ ^ 
v/^0.  $2500  for  1  year,  9  months,  18  days  at  5%. 


h 


Some  teachers  prefer  to  use  the  Six  Per  Cent  Method  in  finding  interest 
instead  of  the  Cancellation  Method  used  in  the  preceding  explanation. 
The  Six  Per  Cent  Method  may  be  used  by  teachers  who  prefer  it  or  whose 
course  of  study  requires  it.    This  method  uses  the  following  data: 

The  interest  on  $1  for  1  year     =$.06 
The  interest  on  $1  for  1  month  =  .005 
The  interest  on  $1  for  1  day      =  .000^ 

Find  the  interest  on  $250  for  3  years,  3  months,  18  days  at  6%. 

Interest  on  $1  for   3  years     =  3X.06     =$.18 
Interest  on  $1  for    3  months  =  3  X  .005   =  .015 
Interest  on  $1  for  18  days      =  18  X  .000^  =   .003 
Interest  on  $1  for  the  entire  time      =$.198 
Interest  on  $250  for  3  years,  3  months,  18  days = 250  X$.  198  =$49.50. 

The  interest  at  any  other  rate  than  6%  can  be  found  by  taking  \  of 
the  interest  at  6%  and  multiplying  by  the  given  rate. 

When  the  times  are  stated  for  the  beginning  and  end  of  the 
interest-bearing  period,  the  following  form  is  used  in  determining 
the  time  for  computing  the  interest:     • 


APPLICATIONS   OF  PERCENTAGE— INTEREST  99 

21.  What  is  the  interest  on  a  note  for  $300  dated  April  1, 
1906,  and  paid  May  15,  1908,  at  6%? 

Year.  Month  Day 
1908—  5  —15 
190&—  4—1 
2—  1  —14 

Therefore,  the  time  is  2  years,  1  month  and  14  days.    Com- 
pute the  interest. 

22.  Find  the  interest  on  $200  from  Sept.  26, 1915,  to  Jan.  24, 
1917,  at  6%. 

Year  Month  Day  ^f^Q  can  not  subtract  26  days  from  24 
1916  —  12  —  54  days,  so  we  reduce  1  month,  taken  from 
T9^7 —  X  —  24  the  months  column  to  days,  making  30  days; 
1915—  9  —  26  add  the  30  days  to  the  24  days,  making 
1  —  3  —  28  54  days.  26  days  from  54  days  leaves  28 
days.  We  have  already  used  the  1  month 
in  the  months  column,  so  we  must  take  a  year  from  the  year 
column  (leaving  1916)  and  reduce  it  to  12  months.  12 
months— 9  mo.  leaves  3  months.     1916  —  1915  =  1  year. 

Therefore,  the  time  is  1  year,  3  months,  28  days.    Compute 
the  interest. 

Find  the  interest  on: 

23.  $750  from  April  7,  1915,  to  July  14,  1917,  at  6%. 

24.  $350.Y5  from  Dec.  18,  1912,  to  March  16,  1915,  at  6%. 

25.  $2000  from  Nov.  1,  1916,  to  Jan.  1,  1918,  at  5%. 

26.  $150  from  July  25,  1910,  to  March  15,  1912,  at  7%. 

27.  $275  from  Oct.  9,  1913,  to  March  3,  1915,  at  6%. 

28.  $5000  from  Aug.  16,  1916,  to  August  16,  1921,  »t  5%. 

29.  $500  from  May  22,  1914,  to  Sept.  22,  1917,  at  6%. 


100 


SEVENTH  YEAR 


30.  $850  from  Mar.  1,  1915,  to  Oct.  5,  1916,  at  6%. 

31.  $425  from  Feb.  10,  1917,  to  Mar.  13,  1918,  at  6%. 

32.  $1500  from  Jan.  12,  1916,  to  July  3,  1917,  at  5%. 

33.  $236.25  from  Dec.  6,  1916,  to  Oct.  12,  1917,  at  6%. 

34.  I  borrowed  $300  on  July  18,  1916,  at  6%,  promising  to 
pay  the  note  on  demand.  The  owner  presented  the  note  for 
payment  on  April  21,  1917.  How  much  interest  was  there  on 
the  note  at  that  time?   What  was  the  total  sum  due  the  lender? 

Bankers  and  other  firms  who  have  a  great  deal  of  interest  to 
compute  use  tables  in  order  to  save  time  and  insure  greater 
accuracy.  The  following  interest  table  was  computed  on  the 
basis  of  360  days  to  the  year.  Some  tables  are  computed  on 
the  basis  of  365  days  to  the  year  if  the  exact  interest  is  wanted. 


INTEREST  ON  $1.00 

Time 

5% 

6% 

7% 

1 

$.000139 

$.000167 

$.000194 

2 

.000278 

.000333 

.000389 

3 

.000417 

.000500 

.000583 

00 

>> 

4 

.000556 

.000667 

.000778 

a 

5 

.000694 

.000833 

.000972 

6 

.000833 

.001000 

.001167 

7 

.000972 

.001167 

.001361 

8 

.001111 

.001333 

.001556 

9 

.001250 

.001500 

.001750 

10 

.001389 

.001667 

.001944 

20 

.002778 

.003333 

.003889 

1 

.004167 

.005000 

.005833 

CO 

2 

.008333 

.010000 

.018667 

-k2 

3 

.012500 

.015000 

.017500 

O 

4 

.016666 

.020000 

.023333 

5 

.020833 

.025000 

.029167 

6 

.025000 

.030000 

.035000 

1  Year 

.050000 

.060000 

.070000 

APPLICATIONS   OF  PERCENTAGE— INTERESTlOl 

Exercise  6 

1.  Find  the  interest  on  $200  for  2  years,  3  months,  13  days 
at  6%,  using  the  above  table: 

Interest  on  $1.00  for   2  years     =$.12 
Interest  on  $1 .00  for    3  months  =    .015 
Interest  on  $1.00  for  10  days      =    .001667 
Interest  on  $1.00  for    3  days      =    .0005 
Interest  on  $1.00  for  total  time  =$.137167 
Interest  on  $200  for  the  given  time,  200X$.137167  =  $27.43+. 
Using  the  interest  table,  find  the  interest  on: 

2.  $300  for  1  year,  6  months  at  6%. 

3.  $250  for  1  year,  4  months,  20  days  at  7%. 

4.  $500  for  2  years,  7  months,  9  days  at  5%. 
6.  $75  for  1  year,  6  months,  5  days  at  7%. 

6.  $2000  for  3  years,  6  months  at  5%. 

7.  $700  for  8  months,  25  days  at  6%. 

8.  $100  for  2  years,  9  months,  24  days  at  7%. 

9.  $500  for  1  year,  2  months,  23  days  at  6%. 
10.  $375  for  3  years,  6  months  at  6%. 

PARTIAL  PAYMENTS 

When  a  note  is  given  for  a  long  period,  the  interest  is  usually 
to  be  paid  periodically,  and  not  to  be  deferred  until  the  principal 
becomes  due.  A  part  of  the  principal  may  likewise  be  paid 
from  time  to  time.  Such  a  payment  is  called  a  partial  payment. 
The  amount  paid  should  be  stated  on  the  back  of  the  note, 
together  with  the  date  on  which  it  is  received. 

The  subject  of  Partial  Payments  in  Arithmetics  is  one 
in  which  there  has  been  much  confusion,  owing  to  the  diverse 


102  SEVENTH  YEAR 

laws  of  different  states.  The  tendency  is  towards  unity  of 
practice  in  partial  payments,  since  nearly  all  of  the  states  have 
adopted  this  rule  sustained  by  the  Supreme  Court  of  the 
United  States  in  cases  that  have  come  before  it.  This  is 
known  as  the  United  States  Rule,  and  is  in  substance  as  follows: 

When  a  partial  payment  or  the  sum  of  two  or  more 
partial  payments  is  equal  to,  or  more  than,  the  interest 
due,  it  is  to  be  subtracted  from  the  amount  {principal 
-\- interest  due)  at  the  time;  and  the  remainder  is  to  be 
considered  a  new  principal,  from  that  time  to  the 
next  payment. 

The  following  form  shows  the  method  of  recording  partial 
payments  on  a  note  :^ 


QlfiyU^,/TMQ/l^_,_    afterdate Cil_.._ ^promise  to  pay  to 

the  order  of  .,.,hfinV_V(yp__G^  

with  interest  at V^..(9j.... for  value  received. 

^6^cAa^j^?(>'_ 


f^ji/cii/utdj  oruiJm^/naGj: 
luJ^Yll'IK^^SO.    QofvrvDoV 

^.1^17^75.  pfwvJOoC 
)cu7V.J,  ISI8  ^100.  phrulOoo 

^Payments  on  a  note  are  usually  made  at  interest-bearing  dates.  If  the 
interest  is  payable  on  Jan.  1  and  July  1  of  each  year,  it  is  often  specified 
ihat  partial  payments  may  be  made  on  those  dates. 


APPLICATIONS  OF  PERCENTAGE  103 

Exercise  7 

1.  Find  the  amount  of  the  note  on  p.  102,  due  on  settle- 
ment at  maturity. 

Solution: 

$400.00  1st  principal. 

24.00  interest  from  July  1,  1915,  to  July  1,  1916. 

424.00  amount  due  July  1,  1916. 

50.00  payment  July  1,  1916. 

374.00  new  principal. 

11.22  interest  from  July  1,  1916,  to  Jan.  1,  1917, 

385.22  amount  due  Jan.  1,  1917. 

75.00  payment  Jan.  1,  1917. 

310.22  new  principal. 

18.61  interest  from  Jan.  1,  1917,  to  Jan.  1,  1918. 

328.83  amount  due  Jan.  1,  1918. 

100.00  payment  Jan.  1,  1918. 

228.83  new  principal. 

6.86  interest  from  Jan.  1,  1918,  to  July  1,  1918. 

$235.69  amount  due  on  note  at  date  of  maturity. 

2.  Find  the  amount  due  at  maturity  Jan.  15,  1918,  on 
a  note  drawn  at  Indianapolis,  Ind.,  Jan.  15,  1916,  for  $1000 
with  interest  at  6%,  having  the  following  credits  indorsed 
upon  it: 

July  15,  1916,  $80.     Jan.  15,  1917,  $107.     July  15,  1917,  $29. 

3.  What  was  due  at  maturity,  Aug.  10,  1917,  on  a  note 
drawn  at  San  Francisco,  Cal.,  Feb.  10,  1915,  for  $650  with 
interest  at  6%,  having  the  following  partial  payments  indorsed 
upon  it? 

Aug.  10,  1915,  $109.50.        Aug.  10,  1916,  $219.50. 
Feb.  10,  1916,  $116.50.        Feb.  10,  1917,  $50.00 

4.  What  amount  was  due  at  maturity  July  15,  1917, 
on  a  note  drawn  at  St.  Louis,  Mo.,  July  15,  1915,  for  $800 
with  interest  at  5%,  having  these  credits  indorsed  upon  it? 
Jan.  15,  1916,  $210.     July  15,  1916,  $215.     Jan.  15,  1917, 


104 


SEVENTH  YEAR 


COMMISSION 

If  a  fruit  grower  or  farmer  wishes 
to  sell  his  produce  in  a  distant  city, 
he  can  not  usually  afford  to  leave 
his  work  and  go  to  the  city  to  attempt 
to  find  a  buyer.  It  is  more  profitable 
for  him  to  have  some  firm  in  the  city 
sell  the  produce  for  him.  Refrigerator 
cars  now  make  it  possible  to   ship 

fruits  and  vegetables  thousands  of  miles  to  distant   cities 

where  higher  prices  can  be  secured  for  them. 

There  are  two  ways  in  which  the  grower  can  dispose  of  his 
products:  (1)  he  can  sell  directly  to  some  wholesale  firm  or 
(2)  he  can  consign  it  to  a  commission  firm  to  sell  for  him  at 
a  certain  per  cent  of  the  sale. 

If  the  grower  sells  directly  to  a  firm,  he  usually  sends  a  sight 
draft  attached  to  a  bill  of  lading,  making  it  necessary  for  the 
firm  to  pay  the  draft  before  they  can  secure  the  bill  of  lading 
and  get  possession  of  the  goods  from  the  railroad  company. 

This  sight  draft  can  be  deposited  by  the  grower  with  the 
local  bank  for  collection.  The  local  bank  then  sends  this 
draft  to  a  bank  in  the  city,  where  the  debtor  does  business, 
for  collection.  It  is  customary  for  the  local  bank  to  allow  the 
grower  to  check  against  the  amount  of  the  draft,  but  he  must 
replace  the  money  if  the  draft  is  refused  by  the  firm  to  which 
he  sent  the  goods. 

If  a  grower  asks  a  commission  firm  to  sell  the  goods  for 
him,  he  consigns  the  shipment  to  them  and  they  dispose  of 
it  to  the  best  advantage,  charging  a  certain  commission  for 
their  work.  After  deducting  commission,  freight,  cartage, 
storage  or  any  other  necessary  expenses,  the  commission  firm 
sends  the  proceeds  to  the  shipper. 


APPLICATIONS  OF  PERCENTAGE— COMMISSIONS105 

Wheat,  corn  and  other  grains  are  bought  and  sold  in  large 
cities  in  hoards  of  trade  where  the  members,  called  brokers,  are 
required  to  pay  for  the  privilege  of  buying  and  selling  produce. 

Exercise  8 

1.  A  fruit  grower  in  Michigan  consigned  to  a  commission 
firm  in  Chicago  240  barrels  of  apples  to  be  sold  to  the  best 
advantage.  The  freight  charges  were  12^  per  100  lb.  and  the 
apple  barrels  were  considered  as  weighing  160  lb.  each.  Find 
the  amount  of  the  freight  charges. 

2.  The  cartage  (or  drayage)  on  these  apples  amounted  to  Gff 
per  barrel.    Find  the  cartage  charges. 

3.  128  barrels  were  placed  in  cold  storage  at  the  rate  of  15^ 
for  the  first  month  and  12^  for  each  month  thereafter.  80 
barrels  were  sold  out  of  cold  storage  during  the  first  month  and 
the  remainder  during  the  second  month.  Find  the  storage 
charges.^ 

4.  The  following  sales  were  made:  60  bbl.  of  Wolf  Rivers 
at  an  average  of  $4.25  per  bbl.;  35  bbl.  of  Baldwins  at  $3.75 
per  bbl.;  52  bbl.  of  Northern  Spys  at  $5.00  per  bbl.;  93  bbl. 
of  Greenings  at  $3.50  per  bbl.  What  was  the  commission  on 
the  total  sales  at  7%? 

6.  After  deducting  the  commission,  storage,  cartage  and 
freight,  find  the  proceeds  which  the  commission  firm  sent  to 
the  shipper. 

6.  A  potato  grower  sold  a  carload  of  potatoes  consisting 
of  240  even-weight  sacks  of  150  lb.  each  at  80  cents  a  bushel. 
What  did  he  receive  for  the  carload?    (1  bu.  potatoes  =  60  lb.) 

7.  The  buyer  paid  freight  at  the  rate  of  27  cents  per  hundred 
pounds.    What  was  the  freight  bill? 

*Any  fraction  of  a  month  counts  as  a  whole  month  in  computing  storage. 


106  SEVENTH  YEAR 

8.  James  Condon  of  New  Jersey  had  186  bbl.  of  sweet 
potatoes  which  he  wished  to  sell.  He  wired  his  broker  in  Detroit, 
Mich.,  to  sell  them  to  the  best  advantage.  The  broker  was 
offered  $3.25  per  bbl.  F.  O.  B.  loading  pomt.  This,  Condon 
accepted.  How  much  did  Condon  receive  for  the  carload  of 
potatoes? 

9.  How  much  must  he  send  his  broker  at  15jif  per  bbl. 
•   brokerage? 

10.  What  were  Condon's  net  proceeds  on  the  sale? 

^  11.  A  woman  canvasser  sells  an  improved  kitchen  utensil 
on  a  commission  of  15%.  What  must  be  the  amount  of  the 
sales  to  pay  her  $30.00? 

12.  An  administrator  for  an  estate  of  $750,000  gave  a  bond 
for  double  that  amount.  The  premium  of  the  bond  was  $1185. 
The  agent  securing  the  bond  received  a  commission  of  15% 
of  the  premium.    What  was  his  conunission? 

13.  A  firm  bought  42,070  lb.  of  onions  in  111.  at  75^  per  bu. 
of  57  lb.  and  sold  them  in  Michigan  at  95  ji  per  bu.  of  54  lb. 
They  paiJ  freight  at  the  rate  of  li  per  100  lb.  How  much  was 
the  firm's  actual  gain  on  the  onions? 

14.  If  a  travelling  salesman  receives  a  commission  of  10% 
on  his  sales,  what  will  be  the  amount  of  his  commission  if  his 
yearly  sales  amount  to  $25,000? 

16.  A  real  estate  agent  sells  a  building  for  $15,500,  receiving 
a  commission  of  3%.    What  does  he  receive  for  his  services? 

16.  A  collector  remits  to  his  customer  $114  after  deducting 
a  commission  of  5%.    How  much  did  he  collect? 

17.  A  produce  broker  received  $927  to  invest  in  potatoes 
at  90^  per  bushel,  on  a  commission  of  3%.  How  many  bushels 
did  he  buy?i 

^First  find  the  cost  of  each  bu.  of  potatoes,  including  the  commission. 


APPLICATIONS  OF  PERCENTAGE— TAXES      107 

18.  A  farmer  placed  2000  bu.  of  new  corn  in  crib  in  Novem- 
ber, 1915,  to  be  sold  by  a  commission  firm  when  the  price 
reached  85  jz^  per  bu.  This  corn  was  sold  at  that  price  in  June, 
1916.  The  shrinkage  on  the  corn  was  12%.  The  commission 
was  5%.    Find  the  amount  of  the  commission. 

19.  A  real  estate  agent  sold  a  farm  for  $20,000,  receiving 
for  his  services,  from  the  owner,  a  commission  of  2%.  What 
was  the  amount  of  his  commission? 

20.  A  real  estate  agent  purchased  a  farm  for  a  customer, 
and  added  to  the  price  5%  commission.  His  bill  was  what  per 
cent  of  the  price  he  paid?  The  bill  was  for  $10,500.  What  was 
the  price  paid? 

21.  Having  deducted  $5.00  for  expenses,  and  $45.50  for 
commission  at  5%,  a  commission  merchant  forwarded  to  his 
principal  the  remainder  of  the  cash  received  for  a  consignment 
of  farm  products.  What  amount  was  remitted  to  the  con- 
signor? 

22.  A  broker  receives  $4010  to  be  invested  in  wheat  at 
$1.00  per  bushel,  his  commission  being  j%  for  making  the 
purchase.  What  will  his  customer  pay  for  each  bushel  so 
purchased?  How  many  bushels  can  be  purchased  for  the 
amount  stated? 

TAXES 

The  state,  the  county,  the  city  and  the  school  district  must 
have  funds  to  pay  the  expenses  of  the  officers  and  laborers  who 
render  services  to  those  divisions  of  government. 

1.  What  are  some  of  the  services  that  the  officers  of  the 
city  perform  for  the  people  in  that  city? 

2.  What  benefits  do  the  inhabitants  of  a  school  district 
get  from  the  funds  spent  for  school  purposes? 

3.  How  do  the  state  and  county  governments  serve  the 
people? 


108 


SEVENTH  YEAR 


The  funds  necessary  for  carrying  on  the  government  of  the 
state  and  various  local  divisions  are  usually  raised  by  taxing 
the  people  on  the  amount  of  property  which  they  own. 

Property  is  divided  into  two  classes:  (1)  real  estate,  includ- 
ing lands  and  buildings;  and  (2)  personal  property,  consisting 
of  movable  possessions  such  as  clothing  and  jewelry,  household 
furnishings,  domestic  animals,  and  farm  products,  the  merchan- 
dise and  productions  of  stores  and  shops,  machines  and  engines, 
vehicles,  mortgages  and  notes,  stocks  and  bonds,  money,  etc. 

Officers,  generally  called  assessors,  determine  the  value  of 
the  property.  Then  the  proper  officers  of  each  local  division 
of  government  estimate  the  amount  of  money  that  they  will 
need  to  carry  on  the  government  of  their  division  for  the  next 
year.  This  levy  is  turned  in  to  some  county  or  state  officer 
who  divides  the  levy  by  the  assessed  valuation  of  the  property 
to  find  the  rate  of  taxation  for  each  local  division.  Collectors 
then  collect  the  proper  amount  from  each  person  according 
to  the  amount  of  his  property.  The  following  table  gives  an 
illustration  of  the  manner  in  which  the  various  rates  of  taxation 
are  computed: 


HOW  THE  TAX  RATES  ARE  COMPUTED 


Division  of 
Government 

Levy 

Assessed  Valua- 
tion of 
Property^ 

Rate  of  Taxa- 
tion =  Levy  -j- 
Assessed  Val. 

State 

$19,994,495.11 

198,703.42 

1,500.00 

4,000.00 

14,259.27 

$2,499,311,888 

42,277,324 

1,228,410 

295,443 

534,055 

.0080 
.0047 
.0012  + 
.0135+ 
.0267+ 

County 

Town 

City 

School  District 

Total  Rate  of  T 

axation 

.0541  + 

*  Assessed  valuation  of  the  property  in  this  state  is  taken  as  J  of  the 
actual  value.     Systems  of  taxation  vary  in  different  states. 


APPLICATIONS  OF  PERCENTAGE— TAXES     109 

Exercise  9 

1.  What  would  be  a  man's  taxes  who  lived  in  all  these 
divisions  if  his  property  was  assessed  for  $15,350? 

Compute  the  amount  of  tax  in  each  local  division  and  then  find  the 
total.    Why  must  a  collector  compute  these  various  amounts  separately? 

2.  What  is  the  rate  of  taxation  in  your  county  for  county 
purposes?  In  your  state  for  state  purposes?  In  your  school 
district  for  school  purposes? 

Appoint  some  one  in  the  class  to  get  this  information  from  the  collector, 
the  county  clerk,  or  consult  a  tax  receipt. 

3.  If  property  is  taxed  at  the  rate  of  $5.50  per  $1000, 
what  is  the  per  cent  of  taxation?  How  many  mills  is  that  on 
the  dollar? 

4.  In  a  certain  village  the  assessed  valuation  of  the  property 
is,  in  round  numbers,  $300,000.  The  amount  of  tax  needed 
for  carrying  on  the  government  is  $5000.  What  will  be  the  rate 
of  taxation  for  village  purposes? 

5.  A  school  board  estimates  that  the  expenses  of  running 
their  school  will  be  $4500  and  make  a  levy  for  that  amount. 
If  the  assessed  valuation  of  the  property  in  the  district  is 
$350,000,  what  will  be  the  rate  of  the  school  tax? 

6.  The  assessed  valuation  of  a  tract  of  land  adjoining  a 
city  is  valued  at  $15,000  and  the  present  rate  of  taxation  is 
1,5%.  If  the  land  is  annexed  to  the  city  in  which  the  rate  of 
taxation  is  2.5%,  what  will  be  the  increase  in  the  taxes  of  the 
owner  of  the  land?  What  benefits  will  he  receive  for  the  extra 
taxes  that  he  pays? 

7.  If  the  assessed  value  of  the  property  in  a  certain  county 
is  $18,596,482  and  the  total  taxes  levied  upon  it  for  state  and 
local  purposes  is  $650,876.87,  what  is  the  total  rate  of  taxation? 

8.  In  a  certain  township  (town)  a  tax  of  $20,000  is  to  be 


110  SEVENTH  YEAR 

raised.    If  there  are  500  citizens  to  pay  a  poll  tax  of  $1  each, 
how  much  of  the  tax  must  be  laid  on  property? 

A  poll  tax  is  a  small  tax  levied  on  males  without  regard  to 
their  property.  "Poll"  means  head;  that  is,  the  tax  is  so  much 
a  head.  Poll  taxes  are  being  abolished  in  many  places.  Find 
whether  your  community  still  has  a  poll  tax. 

9.  A  man  has  $1200  loaned  out  at  6%  interest.  He  is 
assessed  on  -j  the  amount  of  his  loan  and  the  rate  of  taxation 
is  4^%.  How  much  will  be  his  net  returns  each  year  on  the 
loan  after  he  pays  his  taxes? 

10.  In  a  village  containing  propeity  assessed  at  $200,000, 
the  rate  of  taxation  is  3%.  If  a  poll  tax  of  $2  can  be  collected 
from  800  citizens,  how  much  can  the  assessed  rate  of  taxation 
be  reduced? 

11.  A  village  levied  $4800  in  taxes  on  property  valued  at 
$600,000.    Find  the  rate  of  taxation. 

SPECIAL  ASSESSMENTS 

If  a  city  wishes  to  pave  a  street,  it  assesses  the  cost  upon  the 
owners  of  the  adjoining  property  because  the  pavement  will 
add  to  the  value  of  the  property.  The  city  usually  pays  for 
the  pavement  of  the  intersections  of  the  street.  Such  assess- 
ments are  called  special  assessments. 

Drainage  ditches  are  also  paid  for  in  special  assessments,  the  amount 
of  the  tax  depending  upon  the  distance  from  the  ditch.  The  owners  of 
land  adjoining  the  ditch  are  benefited  most  and  hence  must  pay  the  highest 
tax. 

If  the  object  of  the  special  assessment  is  equally  beneficial  to  aU  the 
inhabitants  of  the  city,  such  as  parks  and  Ubraries,  the  special  taxes  are 
levied  upon  all  the  property  in  the  city. 

Find  an  example  of  a  special  assessment  that  has  been  levied 
in  your  conmiunity.  How  was  the  tax  assessed?  Make  five 
problems  out  of  the  information  you  secure  on  this  special 
assessment. 


APPLICATIONS  OF  PERCENTAGE— ASSESSMENTS  111 

PROBLEMS 

1.  If  the  assessment  valuation  for  a  certain  city  is  $1,800,000 
and  there  is  to  be  raised  for  a  special  purpose  $48,000,  what  will 
be  the  rate  of  taxation  required  for  this  purpose? 

2.  What  will  this  add  to  the  tax  of  a  resident  who  owns 
property  assessed  at  $6000? 

3.  A  drainage  district  was  formed  for  reclaiming  some  of 
the  low  land  along  the  Illinois  River.  The  area  drained  was 
1280  acres.  The  cost  of  the  work  was  $25,600.  What  was  the 
assessment  on  each  acre  if  the  amount  was  equally  distributed? 

4.  The  streets  of  a  city  are  being  paved  at  a  cost  of  $1.20 
per  sq.  yd.  The  width  of  the  paving  is  30  feet.  The  cost  of 
the  curbing  is  60  cents  per  running  foot.  How  much  will  be  the 
tax  on  a  man  owning  a  frontage  of  50  feet  if  he  is  required  to 
pay  for  the  pavement  to  the  middle  of  the  street? 

6.  What  will  be  the  assessment  on  the  owner  of  a  comer 
lot  in  the  same  city  if  his  lot  is  150  feet  long  and  45  feet  wide? 
The  city  pays  for  the  intersections  of  the  streets. 

EXPENSES  OF  THE  NATIONAL  GOVERNMENT 

The  principal  items  in  the  yearly  expenses  of  the  national 
government  in  a  recent  year  were  as  follows: 

EXPENSES 

Treasury  Department $     227,277,657.81 

War  Department 8,995,880,266.18 

Navy  Department 2,002,310,785.02 

U.  S.  Shipping  Board 1,820,606,870.90 

Miscellaneous • 1,889,773,159.71 

Total .-.$14,935,848,739.62 

Money  must  be  raised  by  our  national  government  to  meet 
these  expenses.  The  main  sources  from  which  the  national 
government  derives  its  income  are: 


112  SEVENTH  YEAR 

RECEIPTS 

Customs  Duties $    183,428,624.71 

Internal  Revenue 1,239,468,260.01 

Income  and  Excess  Profits  Taxes 2,600,762,734.84 

Interest  on  Obligations  of  ForeignGovemments     322, 162,228.04 

Miscellaneous  Receipts 301,782,004.86 

Total  Ordinary  Receipts $4,647,603,852.46 

Where  does  the  money  come  from  to  meet  the  difference 
between  the  expenditures  and  the  ordinary  receipts  of  the 
government?    (See  page  221.) 

CUSTOMS  DUTIES 

Congress  has  the  authority  to  fix  the  duties  on  imports.  They 
pass  a  law  enumerating  various  schedules  or  classes  of  articles 
and  give  the  duty  on  each  item  in  a  schedule.  Such  a  law  is 
called  a  tariff. 

Since  tariffs  are  frequently  discussed  in  political  campaigns, 
you,  as  future  voters,  should  understand  how  a  duty  is  levied 
and  its  effect  upon  prices  in  this  country. 

Suppose  that  it  costs  $1.00  per  yard  to  make  a  certain  grade 
of  cloth  in  Europe.  If  the  duty  on  this  kind  of  goods  is  35% 
of  the  value  of  the  cloth,  the  duty  will  amount  to  35  cents  per 
yard.  Since  the  importer  can  not  afford  to  lose  this  duty  of 
35  cents,  he  must  sell  his  cloth  in  the  United  States  for  at  least 
$1.35  per  yard. 

1.  Suppose  on  the  other  hand  that  it  costs  $1.35  to  manu- 
facture the  same  grade  of  cloth  in  the  United  States.  Can 
our  factories  compete  with  the  European  goods  after  the 
importers  pay  the  tax  of  35%? 

2.  Could  our  factories  compete  with  the  European  manu- 
facturer of  that  grade  of  cloth  if  he  only  had  to  pay  a  duty  of 
20%? 

3.  Could  the  importer  compete  with  our  factories  if  he  had 
to  pay  a  duty  of  60%  on  the  cloth? 


APPLICATIONS  OF  PERCENTAGE— REVENUE     113 

Since  a  duty  of  35%  in  the  above  illustration  protects  our 
factories  against  the  lower  prices  of  imported  goods  from  Europe, 
it  is  said  to  be  a  'protective  duty.  The  principal  discussions  in 
political  campaigns  have  been  over  raising,  lowering  or  main- 
taining the  tariff  duties  then  in  force. 

In  1916,  Congress  passed  a  law  creating  a  tariff  commission 
to  consist  of  representatives  from  the  leading  political  parties 
of  our  country.  This  commission  is  to  determine  accurately 
the  costs  of  production  of  various  articles  in  the  United  States 
and  in  foreign  countries  and  to  report  this  information  to  Con- 
gress. This  should  enable  Congress  to  form  a  much  better  list 
of  tariff  schedules  than  it  has  done  in  the  past. 

Not  all  imports  are  taxed.  There  are  some  necessities  that 
we  want  to  encourage  people  to  ship  to  this  country  and  we 
allow  them  to  come  in  free.  Among  the  articles  on  the  free  list 
are  agricultural  implements,  bibles,  coffee,  corn,  cotton,  hides, 
meats,  potatoes,  salt,  wool,  milk  and  cream. 

Tariff  duties  are  of  two  kinds,  ad  valorem  and  specific.  Ad 
valorem  duties  are  those  levied  against  the  value  of  the  goods 
imported.  Specific  duties  are  duties  based  upon  the  number, 
weight,  etc. 

For  example,  if  a  duty  on  dress  goods  is  30%  of  the  value  of 
the  goods,  such  a  duty  is  said  to  be  an  ad  valorem  duty.  If  the 
duty  is  5  cents  per  pound,  the  duty  is  said  to  be  specific. 

Ad  valorem  duties  are  more  difficult  to  levy  than  specific  duties  because 
the  goverment  must  keep  experts  who  can  accurately  judge  the  quaUty  of 
the  various  kinds  of  goods.  Specific  duties  on  the  other  hand  are  easily 
levied  because  the  quantity  expressed  in  yards,  pounds,  gallons,  etc.,  has 
merely  to  be  measured.  Specific  duties,  however,  have  the  disadvantage 
of  putting  the  heaviest  burden  on  the  cheaper  grades  of  goods. 

If  the  duties  are  too  high,  foreign  goods  will  not  be  imported 
and  there  will  be  a  decrease  in  the  amount  of  revenue  obtaiDed 
from  customs  duties. 


114 


SEVENTH  YEAR 


Among  the  many  duties  of  the  Tariff  Act  of  1913  are  the 
following: 


Article 

Schedule 

Duty 

Ink  Powders 

A 

15%  ad  valorem. 

Window  Glass 

B 

Ic  per  lb.  between  154  and  384  sq.  in. 

Automobiles 

C 

Over  $2000—45%  ad  valorem.     Less 
than  $2000—30%  ad  valorem. 

Mahogany  Lumber 

D 

10%  ad  valorem  in  rough  boards. 

Horses 

G 

10%  ad  valorem. 

Beans 

G 

25c  per  bu.  of  60  lb. 

Value  up  to  70c  per  doz.,   30%  ad 

Cotton  Stockings .  . 

I 

valorem.    More  than  $1.20  per  doz., 

50%  ad  valorem. 

Wool  Clothing 

K 

35%  ad  valorem. 

Silk  Clothing 

L 

50%  ad  valorem. 

Writing  Paper 

M 

25%  ad  valorem. 

Firecrackers 

N 

6c  per  lb. 

Roman  Candles 

N 

10c  per  lb. 

Cut  Diamonds .... 

N 

20%  ad  valorem. 

Typewriters 

Free  List 

No  duty. 

Potatoes 

Free  List 

No  duty. 

Tell  which  of  the  above  duties  are  ad  valorem  and  which  are 
specific. 

Goods  are  classed  under  different  schedules.  For  instance, 
Schedule  A  includes  chemicals,  oils,  and  paints;  Schedule  G 
includes  agricultural  products  and  provisions,  etc.  Similar 
articles  are  grouped  together  in  the  same  schedule.  The  letters 
of  the  alphabet  A  to  N  are  used  to  designate  the  different 
schedules. 

Exercise  10 
Use  the  preceding  table  to  find  the  corresponding  duties. 
1.  Find  the  duty  on  a  French  automobile  costing  $2500. 


APPLICATIONS  OF  PERCENTAGE— REVENUE     115 

2.  Find  the  duty  on  an  imported  automobile  costing  $1500. 

3.  I  buy  a  team  of  work  horses  in  Canada  for  $300.  How 
much  duty  must  I  pay  to  bring  them  into  this  country? 

4.  A  firm  in  New  York  buys  from  a  firm  in  London  the 
following  goods:  20  reams  of  writing  paper  @  50^  per  ream; 
100  lb.  of  firecrackers;  100  lb.  of  Roman  Candles;  3  typewriters 
@  $60  each.   Find  the  total  amount  of  the  duties  on  these  goods. 

5.  If  I  buy  2000  ft.  of  mahogany  lumber  in  Central  America 
at  $50  per  M  and  import  it  into  this  country,  how  much  duty 
shall  I  have  to  pay? 

6.  A  firm  imports  the  following  bill  of  goods:  3  dozen  silk 
handkerchiefs  @  $3.95  per  dozen;  50  ready-made  wollen  dresses 
at  $12  each;  6  dozen  cotton  stockings  at  $1.80  per  dozen. 
Find  the  total  duties  on  this  bill  of  goods. 

7.  A  jeweler  imported  cut  diamonds  to  the  value  of  $50,000. 
How  much  import  duties  did  he  pay? 

8.  A  firm  imported  10  bags  of  beans  weighing  120  lb. 
each  and  20  sacks  of  potatoes  weighing  150  lb.  each.  Find  the 
amount  of  his  duty. 

9.  A  school  supply  firm  imported  ink  powder  invoiced  at 
$2500  in  Liverpool,  England.  How  much  duty  did  they  pay 
on  this  bill  of  goods? 

10.  A  glass  firm  imports  window  glass  in  sizes  from  154  sq. 
in.  to  384  sq.  in.  If  the  glass  weighed  1000  lb.,  how  much 
duty  did  they  pay  on  the  shipment? 

INTERNAL  REVENUE 

Another  important  source  of  revenue  for  the  government  is 
the  income  from  internal  duties  or  excises  which  are  levied  on 
certain  kinds  of  manufactured  products  as  substitutes  for 
butter,  tobacco  goods  and  non-beverage  distilled  spirits. 


116  SEVENTH  YEAR 

During  the  World  War  the  expenses  of  the  national  govern- 
ment were  extremely  heavy.  In  order  to  meet  these  increased 
expenses  Congress  levied  special  revenue  taxes  which  will  be 
removed  when  the  expenses  are  reduced.  Among  these  special 
taxes  are:  railroad  tickets,  express  and  freight  bills;  telegraph, 
telephone,  and  radio  messages;  automobiles;  admissions  to 
theatres,  concerts  and  cabarets;  non-intoxicating  beverages, 
including  soft  drinks,  mineral  waters,  etc.;  and  stamps  on 
bonds,  notes,  etc. 

1.  The  total  receipts  from  internal  revenue  for  1919  were 
$3,839,950,612.  This  was  an  increase  of  $145,330,973  over  the 
receipts  for  1918.    What  was  the  per  cent  of  increase? 

Income  Taxes 

The  sixteenth  amendment  to  the  Constitution  of  the  United 
States,  adopted  in  1913,  gave  Congress  the  authority  to  levy  an 
income  tax.  The  income  tax  in  force  Jan.  1,  1920,  allows  an 
exemption  (or  deduction)  from  a  person's  net  income  of  $1000 
for  a  single  person  and  $2000  for  a  married  person.  An  addi- 
tional exemption  of  $200  is  allowed  for  each  child  under  18  years 
of  age,  and  also  for  any  other  dependent  who  is  mentally  or 
physically  defective. 

In  computing  his  net  income  a  person  is  allowed  to  deduct 
from  the  gross  income  the  expenses  of  conducting  his  business. 
Living  expenses  cannot  be  deducted  in  computing  the  net  in- 
come. 

All  net  income  up  to  $4000  is  taxed  4%.  All  income  above 
$4000  is  subject  to  a  tax  of  8%.  All  income  above  $5000  must 
pay  an  additional  tax,  called  a  surtax.  The  table  showing  the 
rates  for  the  surtax  is  given  on  the  following  page. 

Why  should  a  married  man  have  a  larger  sum  for  exemption 
than  a  single  man? 


SURTAX  RATES  FOR  1919 


117 


Surtax  Rates  for  1919 


Amount  of  Net 
Income 

Rate 

Amount  of  Net 
Income 

Rate 
19% 

Amount  of  Net 
Income 

Rate 

$  6,000 

1% 

$42,000 

$78,000 

37% 

8,000 

2% 

44,000 

20% 

80,000 

38% 

10,000 

3% 

46,000 

21% 

82,000 

39% 

12,000 

4% 

48,000 

22% 

84,000 

40% 

14,000 

5% 

50,000 

23% 

86,000 

41% 

16,000 

6% 

52,000 

24% 

88,000 

42% 

18,000 

7% 

54,000 

25% 

90,000 

43% 

20,000 

8% 

56,000 

26% 

92,000 

44% 

22,000 

9% 

58,000 

27% 

94,000 

45% 

24,000 

10% 

60,000 

28% 

96,000 

46% 

26,000 

11% 

62,000 

29% 

98,000 

47% 

28,000 

12% 

64,000 

30% 

100,000 

48% 

30,000 

13% 

66,000 

31% 

150,000 

52% 

32,000 

14% 

68,000 

32% 

200,000 

56% 

34,000 

15% 

70,000 

33% 

300,000 

60% 

36,000 

16% 

72,000 

34% 

500,000 

63% 

38,000 

17% 

74,000 

35% 

1,000,000 

64% 

40,000 

18% 

76,000 

36% 

1,000,000  + 

65% 

Explanation  of  Table:  Of  the  first  amount  $6000,  the  exemption  for 
the  surtax  is  $5000,  hence  a  person  with  an  income  of  $6000  would  pay  a 
surtax  of  1%  of  $1000.  A  person  with  an  income  of  $8000  would  pay  a 
surtax  of  2%  on  the  income  between  $6000  and  $8000  (or  $2000)  and 
1  %  on  $1000.     The  3%  rate  is  for  the  portion  between  $8000  and  $10,000. 

Exercise  11 

1.  A  married  man  has  an  income  of  $15,000  a  year.     Find 
the  amount  of  his  income  tax,  allowing  exemptions  for  2  children. 
$2000  +  $400  =  $2400,  total  exemptions. 
$15,000  -  $2400  =  $12,600,  net  income. 

4%  of  $4000 $160.00 

8%  of  $8600  ($12,600  -  $4000) 688.00 

10.00 

40.00 

60.00 

80.00 

30.00 


1%  of  $1000  ($6000  -  $5000).. .  . 
2%  of  $2000  ($8000  -  $6000).. .  . 
3%  of  $2000  ($10,000  -  $8000).. , 
4%  of  $2000  ($12,000  -  $10,000) . 
5%  of  $600  (Excess  over  $12,000). 


Total  income  tax $1068.00 


118  SEVENTH  YEAR 

2.  The  net  income  of  a  married  man  is  $9750  per  year.  He 
has  no  children.     Find  his  income  tax. 

3.  The  yearly  income  of  a  single  woman  is  reported  in  her 
tax  schedule  as  $5320.  She  has  one  dependent  to  support. 
Find  her  tax. 

4.  What  is  the  income  tax  of  an  unmarried  man  with  an 
income  of  $7500,  if  he  has  no  dependents? 

6.  A  merchant  has  a  gross  income  of  $8750  per  year.  The 
expenses  of  running  his  business  amount  to  $2500.  He  is 
married,  and  has  a  child  under  18  years  of  age.  Find  the 
amount  of  his  income  tax. 

6.  A  milliner  (unmarried)  has  a  gross  income  of  $6350  per 
year,  and  the  expenses  of  her  shop  amount  to  $2790  a  year. 
Compute  her  income  tax. 

7.  Find  a  married  man's  income  tax  on  a  net  yearly  income 
of  $42,350.  Allow  additional  exemptions  for  3  children  and  1 
other  dependent. 

8.  Find  the  tax  of  a  single  person  on  a  salary  of  $4500. 

9.  Why  should  a  person  with  a  large  income  pay  a  higher 
rate  on  amounts  above  a  certain  sum? 

INSURANCE 

Insurance  is  a  contract  whereby,  for  a  certain  payment  called 
a  premium,  a  company  guarantees  an  individual  or  firm  against 
loss  from  certain  perils.  The  contract  is  stated  in  a  document 
called  a  policy. 

Instead  of  one  person  carrying  all  the  risk  on  his  life  or 
property,  insurance  distributes  the  risk  over  a  large  number  of 
persons  so  that  no  one  person  has  to  bear  an  extremely  heavy 
loss. 

The  most  common  forms  of  insurance  are: 


APPLICATIONS  OF  PERCENTAGE— INSURANCE  119 

Fire  Insurance  insures  against  loss  from  injury  to  property, 
or  destruction  of  it,  by  fire. 

Life  Insurance  insures  a  person  against  loss  through  the 
death  of  another. 

Accident  Insurance  insures  a  person  against  disability  caused 
by  an  accidental  injury  to  him;  and  in  case  of  his  death  from 
the  injury  received,  it  insures  an  indemnity  to  a  specified 
beneficiary. 

Casualty  Insurance,  of  various  kinds,  insures  against  loss 
resulting  from  accidental  injury  to  property,  such  as  live 
stock,  plate  glass,  etc. 

Fidelity  Insurance  insures  against  loss  arising  from  the 
default  or  dishonesty  of  public  officers,  or  of  clerks  or  agents 
in  the  employ  of  the  insured. 

Marine  Insurance  insures  against  loss  by  injury  to,  or  dis- 
appearance of,  ships,  cargoes,  or  freight,  by  perils  of  the  sea. 

FIRE  INSURANCE 

In  order  to  prevent  insurance  from  having  the  nature  of  a 
betting  or  gambling  contract,  an  agent  is  not  supposed  to 
insure  property  for  its  full  value  against  loss  by  fire.  The 
person  whose  property  is  insured  must  bear  a  portion  of  the 
risk  himself. 

The  rate  of  the  premium  is  generally  stated  at  so  much  per 
hundred  dollars  and  varies  according  to  conditions  such  as 
the  kind  of  fire  department,  nearness  to  other  buildings,  con- 
struction of  the  building,  etc.  Most  firms  insure  property 
for  three  years  at  two  and  a  half  times  the  yearly  rate. 

Insurance  on  furniture  is  strictly  construed  in  accordance 
with  the  exact  terms  of  the  policy.  If  the  furniture  is  removed 
at  all  without  express  permission  from  the  building  in  which 
it  is  insured,  the  insurance  fails. 


120  SEVENTH  YEAR 

Exercise  12 

1.  If  I  deem  my  house  worth  $5000,  and  desire  to  insure 
it  for  one  year  for  three-fifths  of  its  value,  what  must  I  pay 
for  the  poUcy  when  it  costs  $7.50  for  each  $1000  of  insurance 
taken? 

2.  A  farmhouse  and  barn  and  other  buildings  pertaining 
to  them,  valued  at  $15,000,  are  insured  for  one  year  for  two- 
thirds  of  their  value,  at  75  cents  for  each  hundred  dollars  of 
insurance.    What  is  the  cost  of  the  policy? 

3.  If  the  furniture  in  my  cottage  is  worth  $1000,  and 
I  wish  to  insure  it  for  60%  of  its  value,  having  to  pay  $1.66f 
for  each  hundred  dollars  of  insurance,  what  will  the  policy  cost 
me? 

4.  A  church  pays,  in  all,  $180  yearly,  for  insurance  to  the 
amount  of  $10,000,  in  each  of  three  separate  companies, 
the  rate  of  insurance  being  the  same  in  each  company.  What 
is  the  rate  of  insurance? 

If  my  house,  insured  for  $4000,  is  destroyed  and  I  am  unable  to  prove 
that  it  was  really  worth  over  $2000,  I  can  recover  from  the  insurance 
company  no  more  than  the  latter  amount. 

6.  If  when  insured  against  fire  for  $5000  it  was  destroyed, 
and  I  can  prove  its  value  only  to  the  amount  of  60%  of  this 
sum,  what  amount  of  compensation  do  I  receive? 

To  insure  a  house  for  three  years  at  a  time,  one  has  to  pay  two  and 
one  half  times  the  rate  for  a  single  year. 

6.  My  insurance  for  a  three-year  period  is  $31.25.  What 
would  have  been  my  insurance  for  a  single  year? 

By  insuring  a  house  for  five  years  at  a  time,  one  has  to  pay  four 
times  the  rate  for  a  single  year. 

7.  If  a  man  pays  $200  for  the  five-year  period,  what  would 
the  insurance  cost  him  for  a  single  year?  For  a  period  of 
three  years?    For  five  separate  periods  of  one  year  each? 


APPLICATIONS  OF  PERCENTAGE— INSURANCE  121 

8.  If  I  have  furniture  insured  for  $1200,  temporarily  stored 
in  an  outbuilding  which  is  not  mentioned  in  my  policy,  and  the 
outbuilding  and  furniture  are  destroyed  by  fire,  what  amount 
can  I  recover  on  my  loss  of  furniture? 

.  9.  A  rug  worth  $150  is  hung  out  in  the  yard  to  air,  and 
is  ruined  by  sparks  from  a  passing  fire  engine.  If  it  formed  a 
part  of  the  household  furniture  that  is  insured  for  $1000, 
can  the  owner  recover  its  value  from  the  insurance  company? 

10.  What  could  be  recovered  if  it  had  been  thus  destroyed 
while  hung  on  a  line  on  a  porch  of  the  residence? 

11.  A  dozen  books  supposed  to  be  rare  and  valuable  are 
insured  for  $1200.  They  are  destroyed  by  fire,  and  it  is  then 
proved  that  they  were  recently  manufactured,  and  of  no  greater 
possible  value  than  $3  apiece.  What  is  the  limit  of  indemnity 
that  the  company  should  pay  for  them? 


Insurance  Applied 

Mr.  Manning  owned  a 
suburban  lot  on  which  he 
contracted  with  a  house 
construction  company  to 
build  a  home  at  a  total 
cost  of  $4500.  On  the 
completion  of  the  new 
home,  Mr.  Manning,  rec- 
ognizing the  importance 
of  proper  protection  to  his  family,  took  out  an  insurance 
policy  on  the  house. 

Exercise  13 

1.  An  insurance  company  insured  the  house  for  80%  of 
its  cost.    Find  the  amount  of  his  policy. 


122  SEVENTH  YEAR 

2.  Why  will  an  insurance  company  not  insure  a  house  at 
its  full  value? 

3.  The  rate  of  insurance  on  this  house  was  72  cents  per 
$100  for  a  "three-year  period."  What  was  the  cost  of  the 
insurance  per  year? 

4.  Mr.  Manning  made  out  an  inventory  of  his  household 
goods  and  estimated  them  to  be  worth  $950.  He  decided  to 
take  out  $800  on  his  household  goods.  Why  was  it  a  good 
plan  to  make  out  an  inventory  of  the  goods  before  insuring? 
What  should  be  done  with  this  inventory? 

5.  The  rate  of  insurance  on  his  household  goods  was  79 
cents  per  $100  for  three  years.  Find  the  amount  of  the  premium 
on  the  household  goods. 

LIFE  INSURANCE 

There  are  two  principal  kinds  of  life  insurance  companies: 
the  "old  line"  companies  and  the  mutual  companies.  The  old 
line  companies  have  worked  out  definite  rates  for  different  ages 
and  the  premium  for  each  year  is  definitely  stated  in  the 
policy.  The  mutual  companies  usually  levy  an  assessment  at 
certain  intervals,  generally  each  month,  to  pay  the  death  claims. 

The  "old  line"  companies  usually  have  several  kinds  of  policies 
fiuch  as  15-payment  life;  20-payment  life;  endowment  policies; 
ordinary  life  policies.  In  the  15-payment  life  policy,  the  person 
insured  makes  fifteen  yearly  payments  at  the  end  of  which 
his  insurance  is  paid  for  the  rest  of  his  life.  The  20-payment 
life,  as  the  title  indicates,  is  paid  for  at  the  end  of  20  yearly 
payments.  An  endowment  policy  usually  requires  a  larger 
premium  and  if  the  insured  person  lives  to  the  end  of  the  period 
named  in  the  policy  he  can  draw  out  the  amount  of  the  policy. 
In  an  ordinary  life  policy  a  definite  yearly  payment  is  required 
each  year  until  the  person  dies.     All  of  these  forms  usually 


APPLICATIONS  OF  PERCENTAGE— INSURANCE  123 

have  a  cash  surrender  value  which  will  be  paid  the  insured 
person  upon  the  surrender  of  the  policy.  Most  policies  also 
have  a  table  showing  the  amount  of  money  which  the  company 
will  loan  on  a  policy. 

Since  the  risk  of  the  death  of  a  person  increases  with  age, 
the  premium  increases  each  year.  It  is  therefore  an  advantage 
to  take  out  insurance  as  early  as  possible.  The  age  nearest 
the  birthday  of  the  person  insured  is  the  age  considered.  A 
medical  examination  is  also  required  to  protect  the  company 
from  undesirable  risks. 

Premiums  per  $1000 


Age 

Ordinary  Life 

20-Payment  Life 

20- Year  Endowment 

20 

$19.21 

$29.39 

$48.48 

21 

19.62 

29.84 

48.63 

23 

20.51 

30.80 

48.96 

25 

21.49 

31.83 

49.33 

27 

22.56 

32.94 

49.73 

30 

24.38 

34.76 

50.43 

35 

28.11 

38.34 

51.91 

40 

33.01 

42.79 

54.06 

45 

39.55 

48.52 

57.34 

50 

48.48 

56.17 

62.55 

Exercise  14 

1.  At  the  age  of  21,  a  man  insured  his  life  for  $2000  on 
what  is  called  the  ordinary  life  plan,  for  an  annual  payment  of 
$39.24.    What  does  he  pay  in  fifteen  years? 

2.  Had  he  deferred  the  insurance  for  five  years,  it  would 
have  cost  him  $44.10  for  each  year.  How  much  more  would 
this  have  been  than  the  amount  the  insurance  actually  did  cost 
him  for  the  same  period  of  ten  years? 

3.  A  man  took  out  a  15-payment  life  policy  for  $1000  at 
the  age  of  30  at  $40.25  for  each  annual  payment.    What  was 


124  SEVENTH  YEAR 

the  total  amount  of  his  fifteen  payments?  How  can  the  com- 
pany afford  to  insure  him  at  an  amount  which  will  yield  less 
than  the  face  of  the  policy? 

4.  A  man  insured  his  life  on  the  endowment  plan  for  $1000 
at  the  age  of  21,  paying  $48.63  annually  for  a  20-year  period, 
and  lived  beyond  the  time  and  received  the  amount  of  the 
policy.    What  was  the  total  amount  of  his  payments? 

6.  What  did  the  insurance  company  receive  to  pay  them 
for  taking  the  risk  of  his  death  during  that  period? 

6.  A  man  took  out  a  20-payment  life  participating  policy 
for  $2000  at  the  age  of  24,  with  a  premium  stated  at  $62.16 
per  year.  If  his  dividends  on  the  policy  amounted  on  an 
average  to  $10  per  year  for  19  years,  how  much  did  the  insurance 
cost  him? 

A  participating  policy  pays  dividends  to  the  holder  after  the  first  year 
according  to  the  profits  of  the  company.  These  dividends  are  usuallj- 
deducted  from  the  premium,  the  insured  person  paying  the  balance  due 
the  company. 

7.  At  the  end  of  the  period,  the  policy  had  a  cash  surrender 
value  of  $994.  If  he  surrendered  his  policy  at  the  end  of  tte 
period,  how  much  will  his  insurance  cost  him  besides  the  interest 
on  his  payments? 

ACCIDENT  INSURANCE 

1.  A  man  has  paid  $18  for  4  years  for  an  accident  insurance 
policy.  Owing  to  an  accident,  he  is  disabled  for  a  period  of 
6  weeks,  during  which  time  he  receives  $25  a  week.  What 
has  been  the  net  financial  value  of  the  insurance  to  him? 
What  has  been  the  net  loss  to  the  insurance  company? 

2.  A  horse  insured  for  $300  is  choked  to  death,  being  ignor- 
antly  tied  with  a  running  noose  of  rope  for  a  halter  about  its 
neck.  Is  the  owner  entitled  to  the  insurance?  If  by  a  com- 
promise 40%  of  the  policy  is  paid,  what  sum  does  the  owner 
receive? 


REVIEW.    PERCENTAGE  125 

Exercise  15.     Informational  Review 

References  refer  to  page  numbers. 

1.  What  is  a  discount?     Define  net  proceeds.     (91) 

2.  Give  two  advantages  of  using  commercial  discounts.  (93) 

3.  What  is  usury?     (96) 

4.  State  the  United  States  Rule  for  partial  payments.  (102) 
6.  If  you  had  a  carload  of  potatoes  to  ship  to  a  large  city 

for  sale,  describe  the  steps  that  would  be  taken  before  you 
received  pay  for  them.     (104) 

6.  Why  do  we  pay  taxes?  What  are  some  of  the  services 
which  we  secure  from  the  money  paid  out  in  taxes?     (107) 

7.  Distinguish  between  real  estate  and  personal  property.  (108) 

8.  Give  the  chief  items  in  the  expenses  of  our  national  gov- 
ernment. State  the  chief  sources  of  income  for  our  national 
government.     (112) 

9.  What  is  a  tariff?     (112) 

10.  What  is  a  protective  duty?     (112-113) 

11.  Explain  the  difference  between  a  specific  and  an  ad  valorem 
duty.  (113)     Which  kind  of  duty  is  easiest  to  pay?  Why? 

12.  What  are  some  of  the  special  taxes  that  were  levied  during 
the  World  War?     (116) 

13.  Describe  the  system  of  levying  our  national  income  tax.  (116) 

14.  Name  and  describe  five  forms  of  insurance.     (119) 

15.  Describe   the   different   kinds   of   Ufe   insurance    poli- 
cies.    (122) 

16.  What  is  a  participating  policy?     (124) 

17.  What  is  accident  insurance?    (124) 

18.  What  income  tax  will  a  married  person  pay  with  a  net 
income  of  $4500,  there  being  no  dependents  in  the  family? 

19.  What  income  tax  will  a  married  person  pay  with  a  net 
income  of  $5750,  there  being  two  children  under  18? 

20.  Find  the  rate  of  insurance  that  your  parents  pay  on  their 
household  goods. 


126  SEVENTH  YEAR 

Exercise  16 

1.  A  farmer  bought  a  horse  for  $120  and  later  sold  it  for 
$200.     What  was  his  per  cent  of  gain? 

2.  Two  buildings  valued  at  $2000  were  destroyed  by  fire. 
The  insurance  received  was  $1500.  What  was  the  per  cent  of 
loss  to  the  owner? 

3.  Lulu  Alphea,  a  yearling  cow  of  Ashburn,  New  York,  pro- 
duced 13,669  pounds  of  milk  from  which  1000  pounds  of  butter 
were  made.  The  per  cent  of  butter  fat  in  butter  is  about  85%. 
Find  the  per  cent  of  butter  fat  in  the  milk  of  this  cow. 

4.  Silk  hose  costing  $1.50  were  sold  at  $2.00.  What  was 
the  per  cent  of  profit?  New  hose  were  bought  for  20%  more 
than  the  cost  of  the  old  stock.  What  must  be  the  selling  price 
of  the  new  hose  in  order  to  yield  the  same  per  cent  of  profit  as 
the  old  stock? 

5.  Mr.  Gleason  built  a  house  for  $2400.  He  sold  it  two 
years  later  for  80%  more  than  it  cost.  What  was  the  selling 
price  of  the  house? 

6.  In  1920  a  certain  grade  of  hard  coal  sold  for  $14.50  in  a 
city  of  the  middle  west.  In  the  winter  of  1919  it  sold  for  $13.30. 
What  was  the  per  cent  of  increase  during  that  year? 

7.  Grace  bought  2  cakes  of  Palmolive  soap  for  18  cents  at  a 
sale.  What  per  cent  had  the  price  been  reduced  for  the  sale  if 
the  regular  price  was  10  cents  a  cake? 

8.  A  girls'  organization,  consisting  of  38  members,  was  as- 
sessed 5  cents  per  member.  What  per  cent  of  this  assessment 
was  left  in  the  treasury  after  a  bill  of  88  cents  for  sending  a 
telegram  was  paid? 

9.  In  selHng  a  house  for  $4900,  a  man  lost  30%.  What  did 
the  house  cost  him? 

10.  A  newsboy  received  30  Saturday  Evening  Posts.  He 
sold  18  of  them  the  first  evening.  What  per  cent  of  the  papers 
did  he  sell  the  first  evening?  What  per  cent  of  the  30  papers 
did  he  have  left  to  sell? 


REVIEW.     PERCENTAGE  127 

11.  A  real  estate  dealer  bought  a  farm  for  $225  an  acre  and 
sold  it  for  $240  an  acre.    What  was  his  per  cent  of  gain  per  acre? 

12.  A  new  house  costing  $4500  was  damaged  by  a  fire  to 
the  extent  of  $3000.  If  the  building  was  insured  for  only  60% 
of  its  value,  what  was  the  owner's  loss? 

13.  Alice  purchased  a  $125  typewriter  on  the  installment 
plan.  She  paid  $25  cash,  10%  of  the  remainder  in  the  next 
payment,  and  20%  of  the  remainder  the  next  pajonent.  ■  What 
did  she  have  left  to  pay? 

14.  Alice  purchased  a  ream  (480  sheets)  of  typewriting  paper 
for  $1.00.  If  she  had  bought  the  paper  in  small  quantities,  it 
would  have  cost  $.01  for  4  sheets.  What  is  the  per  cent  of  gain 
by  buying  this  paper  by  the  ream? 

15.  Irene  was  given  $40  with  which  to  buy  a  dress.  She  paid 
$25.00  for  the  satin,  $4.00  for  the  trimmings,  and  $7.00  for  mak- 
ing. What  per  cent  of  her  allowance  did  she  spend  on  her  dress? 

16.  A  farmer  bought  a  team  of  horses  for  $500.  One  of  the 
horses  died  and  he  sold  the  other  horse  for  $325.  What  per 
cent  did  he  lose  on  this  investment? 

17.  Karl  bought  a  calf  for $12.  Whenitwas2yearsoldhesoldit 
for  $90.  The  expenses  amounted  to  $42.  Find  his  per  cent  of  profit. 

18.  What  is  the  interest  for  6  months  on  $3650  at  6%? 

19.  Mr.  Pelton  owns  two  cottages  at  a  summer  resort.  The 
cottages  are  worth  $900  each.  He  pays  the  state  $25  per  year 
rental  for  each  of  the  two  lots  on  which  they  are  built.  He 
rented  one  for  $150  for  the  season  of  10  weeks.  He  rented  the 
other  to  various  parties  at  $18  a  week  for  the  10  weeks.  Find  the 
per  cent  of  profit  which  he  made  on  the  two  cottages  that  season. 

20.  Mr.  Rose  fisted  his  house  with  a  real  estate  firm.  They 
sold  it  for  $5500  and  charged  3%  for  their  services.  How  much 
did  he  receive  as  the  net  proceeds  of  the  sale? 

21.  Martha  bought  a  suit  at  a  January  clearance  sale  for 
$22.50  which  had  originally  been  marked  $45.  What  was  the 
per  cent  of  reduction? 


128  SEVENTH  YEAR 

22.  Find  the  interest  on  $150  for  60  days  at  6%. 

23.  Mrs.  Rose  has  a  $1000  Victory  Bond  bearing  4f  % 
interest,  payable  semi-annually.  What  is  the  amount  of  each 
interest  payment? 

24.  The  price  of  the  best  grade  of  "No  Protest"  silk  hosiery 
is  $2.70.  A  reduction  of  25%  is  given  on  "seconds."  How 
much  will  two  pairs  of  the  "seconds"  grade  cost? 

25."  Kathryn  paid  $9  for  a  pair  of  shoes.  This  was  25%  of 
what  she  paid  for  a  suit.     What  was  the  cost  of  the  suit? 

26.  A  lawyer  secured  a  loan  of  $3500  for  a  client  and  charged 
him  3%  commission  for  his  services.  What  was  the  lawyer's 
commission? 

27.  Three-fourths  of  a  pound  of  flour  is  required  to  make  a 
pound  loaf  of  bread.     What  per  cent  of  bread  is  flour? 

28.  It  takes  4^  bushels  of  wheat  to  make  a  barrel  of  flour. 
What  per  cent  of  the  wheat  is  used  in  making  flour?  (A  bushel 
of  wheat  =  60  lbs.;  a  barrel  of  flour  =  196  lbs.) 

29.  A  certain  grade  of  canned  peas  sells  at  $1.50  per  dozen  or 
15  cents  per  can  when  bought  in  less  than  dozen  lots.  What 
per  cent  is  saved  by  buying  in  dozen  lots?  . 

30.  What  premium  will  a  man  35  years  old  pay  on  a  20-pay- 
ment  life  insurance  poUcy  for  $3000  at  the  rate  quoted  in  the 
table  on  page  123? 

31.  The  assessed  valuation  of  a  city  residence  is  $7400. 
How  much  taxes  must  the  owner  pay  if  the  rate  is  $24.18  per 
thousand? 

32.  A  davenport  is  Usted  in  a  furniture  catalogue  at  $250. 
What  will  be  the  cost  if  discounts  of  30%,  10%,  and  2%  are 
allowed? 

33.  Find  the  import  duty  on  a  shipment  of  silk  dress  goods 
invoiced  at  $8540.     (See  page  114  for  rates.) 

34.  A  house  worth  $6000  was  insured  for  75%  of  its  value 
at  $30  per  hundred.     What  was  the  premium? 


CHAPTER  V 

BUSINESS  FORMS  AND  ACCOUNTS 

The  Memorandum  or  Salesman's  Slip 


Brown  ^Dujjdn 


nib  iDj^.i2 
*   o.en 

sold  by  (S 


Drygood5 

Suf  falo,  N.Y 


Purchase 
Change 


P/u.Mvtiv  25 
Hum/Uun/JvuJ/ 


00 

en 


36 


20 
25 
/9 


en 


In  bujdng  goods  at  a 
retail  store,  a  salesman's 
slip  or  memorandum  of 
the  purchase  is  usually 
made  by  the  salesman  or 
clerk. 

By  means  of  carbon 
paper  placed  under  the 
sheet  on  which  the  clerk 
is  writing,  a  duplicate  of 
the  slip  is  made.  The 
firm  keeps  one  copy  and 
gives  the  other  copy  to 
the  customer  for  refer- 
ence. 


The  form  indicated  above  shows  one  form  of  such  a 
memorandum.  It  shows  the  items  of  the  purchase,  the  amount 
received  by  the  clerk  and  the  change  given  to  the  customer. 
This  memorandum  should  be  kept  by  the  purchaser  until  he 
is  sure  that  he  does  not  wis  i  to  exchange  any  of  the  goods. 

If  the  purchase  is  charged,  it  is  so  indicated  upon  a  similar 
memorandum  containing  the  customer's  name  and  address. 
This  memorandum  should  be  kept  by  the  customer  to  check  the 
account  when  the  monthly  statement  is  rendered. 

If  printed  forms  of  salesman's  slips  can  be  secured  from  local  stores, 
it  will  save  much  time  in  the  ruling  of  these  forms  by  the  pupils. 


129 


130  SEVENTH  YEAR 

Exercise  1 

1.  I  bought  the  following  items  at  a  grocery  store;  15  lb. 
of  potatoes  for  45  cents;  2  cans  of  corn  @  12  cents  each;  and 

1  doz.  oranges  @  40  cents.    Make  out  the  salesman's  slip  for 
the  customer. 

2.  How  much  change  should  I  receive  if  I  tendered  the  clerk 
a  two-dollar  bill? 

3.  Mrs.  Jones  bought  the  following  articles  at  a  dry-goods 
store;  6  yd.  ribbon  @  18^  per  yd.;  2  spools  of  No.  50  white 
thread  @  5^  per  spool;  10  yards  of  pique  (pe  ka')  @  30«f  per 
yd.;  3  yd.  of  flannel  @  80^  per  yd.  Make  out  the  clerk's 
memorandum  of  the  sale. 

4.  How  much  change  should  Mrs.  Jones  receive  from  a 
ten-dollar  bill? 

6.  I  bought  the  following  household  supplies  at  a  hardware 
store:    1  ironing  board  @  $1.75;  1  pair  of  waffle  irons  @  90^; 

2  aluminum  kettles  @  Q5i  each.    Make  out  a  salesman's  slip 
for  the  sale. 

6.  How  much  change  did  I  receive  from  the  clerk  if  I  ten- 
dered him  a  five-dollar  bill  to  pay  for  the  purchases? 

Make  out  salesman's  slips  for  the  following  orders : 

7.  Mrs.  Stevenson  bought  ^  doz.  plates  No.  4  @  $1.25; 
^  doz.  plates  No.  8  @  $3.00;  ^  doz.  tea  cups  and  saucers  @ 
$3.00  and  ^  doz.  sauce  dishes  at  $1.90. 

8.  Miss  Dillon  purchased  the  following  articles:  1  whisk 
broom  @  35  cents;  1  vanity  case  @  50  cents;  1  set  of  cups  @ 
$2.00;  and  1  shoe  horn  @  50  cents. 

9.  What  are  some  of  the  advantages  of  using  the  memoran- 
dum or  salesman's  slip? 

10.  Make  out  a  sales  slip  with  prices  of  articles  which  you 
Durchased  at  a  store. 


BUSINESS  FORMS  AND  ACCOUNTS 


131 


The  Invoice  or  Bill 

An  invoice  or  bill  is  a  more  formal  account  of  a  tr^insaction 
than  a  salesman's  memorandum.  Invoices  are  sent  to  a  cus- 
tomer by  a  firm  with  each  shipment  of  goods.  The  following 
is  a  modification  of  a  form  used  by  a  large  wholesale  firm: 


This   sate  made  subject  to  conditions  on  back,  of  invoice 

OrcTer  -  835i6         J^j^  ^  COMPANY, 


1/11/17. 


cfoA/  fn  j.B.na« 


QMlncy,  111, 


Kansas  City^  Ho. 

«So/c^   by       A. L.Griggs 
7errr[S  2%  -  lO  days 

Invoiced  3 M.S.  ChecKed  j.c.t. 


Jan. 


11 


4Pc8.HaiB*    XZ/\^* 

4    "      Bacon    A/6§ 

(unwrpd) 
4    "      Cooked  Kama 

9    "      Ziallan  Styla  Kama 


.17 
.23 
.23 
.24 


♦The  abbreviation  12/14,f  means  from  12  to  14  pounds. 

In  the  above  invoice,  the  number  in  the  first  column  at  the 
right  of  the  descriptions  of  the  articles  shows  the  number  of 
pounds.  The  corresponding  numbers  in  the  next  column 
give  the  cost  per  pound.  Multiply  the  cost  per  pound  by  the 
number  of  pounds  and  enter  the  result  in  the  next  column 
which  contains  the  totals  for  each  article. 


Exercise  2 

1.  Extend  the  invoice  shown  above,  filling  in  the  sums  as 
shown  by  the  dots. 

2.  Find  the  net  amount  of  the  bill  if  it  is  paid  within  10 
days.  (Terms  2% — 10  days,  means  that  2%  discount  will 
be  allowed  if  the  bill  is  paid  within  10  days.) 


132  SEVENTH  YEAR 

Extend  the  following  invoices.  You  may  omit  the  headings 
but  make  a  drawing  for  the  rest  of  the  invoice  form : 

3.  2  10#  Carton  Regular  Frankforts 
2  Pieces  Cooked  Pork  Loin 

10  Pieces  Fresh  Ox  Tails 

2  Pieces  Bacon  5  to  8# 

4.  1  Piece  Fresh  Beef  Round 

3  Pieces  Fresh  Pork  Loins 
10  Pieces  Fresh  Spare  Ribs 
15  Pieces  Fresh  Pigs  Feet 

1  Piece  Cooked  Ham 

6.    1  Piece   Fresh  Beef  Ribs 
20  Pieces  Fresh  Spare  Rib 

1  Piece  Fresh  Pork  Loin 

2  Pieces  Cooked  Hams 
l-25#  Plain  Fresh  Pork  Sausage 

6.  1  Fresh  Side  Beef 
8  Fresh  Beef  Shanks 
2  Jelly  L.  Tongue 
2  Boxes  Frankforts 

20#  Polish  Sausage 

Make  out  bills  for  the  following  goods,  using  fictitious  names 
for  the  firm  and  the  purchaser : 

7.  1  parlor  lamp  @  $2.95;  3  glass  candlesticks  @  29f^; 
1  chafing  dish,  $7.50;  2  brass  jardinieres  at  $1.75;  2  vases  at 
$3.00;  2  cut  glass  salt  cellars  at  95jif. 

8.  2  granite  stew  pans  @  39 (if;  2  mufl&n  pans  @  27 j5;  1  can 
opener  @  10 ji;  2  aluminum  measuring  cups  @  10 ji;  2  pair 
scissors  @  75^;  2  butcher  knives  @  50^;  1  electric  iron  @  $3.79. 

9.  1  pair  slippers  @  $2.00;  1  pair  rubbers  @  $1.25;  2  bottles 
gilt-edge  polish  @  25^;  3  pairs  shoe  strings  @  lOjf;  1  pair  ladies' 
shoes  $5.50. 


20 

13i 

8 

31 

10 

8 

11 

25 

93 

14i 

19 

16 

10 

12j 

15 

5 

13 

29 

86 

13i 

10 

12^ 

14 

i5i 

27 

28 

25 

15 

179 

8 

11 

7 

11 

27i 

20 

12i 

20 

11 

BUSINESS  FORMS  AND  ACCOUNTS 


133 


The  Monthly  Statement 

When  salesman's  slips  oi  bills  are  rendered  with  orders, 
the  customer  is  supposed  to  keep  these  forms  with  the  various 
items  shown  on  them  in  order  to  check  the  monthly  statement 
which  is  sent  at  the  end  of  each  month.  The  following  is  one 
form  of  a  monthly  statement  that  is  used : 

When  the  customer  so 
desires,  an  itemized 
statement  will  be  ren- 
dered, but  this  makes  a 
great  deal  of  extra  work 
for  the  firm  and  is  un- 
necessary if  the  customer 
keeps  his  slips  or  bills  to 
check  the  totals  listed 
under  the  various  dates  of  the  monthly  statement. 


Statement          r»^y- 1. "". 

In  Accoutrr'WiTH 

J.S.CLAKKE 

JijLWMKU^Wii. 

Mr*.  Horvey  Buchanan 

Aug. 

1 

Groeariaa 

1 

37 

4 

" 

2 

69 

i 

" 

48 

14 

« 

3 

78 

19 

• 

2 

55 

28 

■ 

1 

30 

30 

m 

3 

25 

15 

62 

Exercise  3 

1.  Make  out  a  monthly  statement  to  Mrs.  F.  R.  Fitzgerald 
from  Adams  Bros.,  Grocers,  for  the  following  grocery  orders, 
showing  only  the  totals  for  each  day: 

Aug.  1:  2  loaves  of  bread  @  15(^;  2  pounds  prunes  @  30^; 
\  pound  cheese  @  40^;  10  pounds  sugar  @  W^. 

Aug.  3 :  \  pound  dried  beef  @  60«5  a  lb. ;  |  dozen  lemons  @ 
40^  a  dozen;  1  peck  potatoes  ^^i. 

Aug.  4:  2  cans  corn  @  18)!f;  1  basket  tomatoes  35^. 

Aug.  9:  Celery  \hi;  1  head  lettuce  15^;   1  package  of  rolled 
oats  28^. 

Aug.  12:  10  bars  soap  79ff;  1  basket  tomatoes  30i^;  1  sack 
flour  $1.50;  1  head  of  cabbage  \%i. 

Aug.  17:  10  pounds  sugar  @  \\i\  2  dozen  eggs  @  38<{;  2 
pounds  butter  @  56^. 


134  SEVENTH  YEAR 

Aug.  20:  1  peck  potatoes  42^;  2  packages  crackers  @  15^; 
1  box  salt  lOj^f. 

Aug.  23:  2  quarts  of  peas  for  25^;  1  package  puffed  rice  15ff; 
10  pounds  apples  @  8^. 

Aug.  26:  1  jar  olives  35^;  2  pounds  navy  beans  @  12)^;  5 
pounds  rice  @  15^. 

Aug.  30:  1  dozen  eggs  38f^;  1  pound  butter  57^;  1  half-pound 
can  cocoa  23^;  1  pound  coffee  45^. 

2.  Make  out  an  itemized  statement  of  the  same  account, 
showing  each  of  the  items  and  the  total  for  each  day. 

3.  Make  out  a  series  of  purchases  from  a  dry-goods  store 
during  some  month  and  render  a  monthly  statement  for  them. 

Receipts 
When  a  sum  of  money  is  paid  on  an  account,  the  customer 
should  receive  a  receipt,  showing  the  date  and  amount  paid 
as  in  the  following  form : 


GALVESTON,  TEXAS,    qJpA'  /5,   TQt  7 

QjJimj  o/jnA^ '  f^    Dollars 

.cm/ n/'X-xnA/nlJ  jp        ■    j        , 


If  the  full  amount  of  the  account  is  paid  instead  of  a  portion 
of  it,  the  words  "m  full  of  account  to  date"  would  be  used  in 
place  of  the  expression  "on  account^" 

If  an  account  is  paid  by  a  check,  the  check  stands  as  a  suffi- 
cient receipt  for  the  payment.  For  this  reason,  many  persons 
pay  all  their  accounts  by  checks. 

This  saves  the  firm  the  trouble  of  making  out  extra  receipts 
or  returning  the  receipted  bill  to  the  customer,  because  the 
cancelled  checks  are  returned  by  the  bank  with  their  monthly 
statement. 


BUSINESS  FORMS  AND  ACCOUNTS  135 

Exercise  4 

1.  R.  A.  Milton  owes  Schneider  &  Co.  $30.25  for  hardware 
supplies.  He  pays  them  $25.00  to  apply  on  his  account. 
Write  a  proper  receipt  for  this  payment. 

2.  J.  R.  Kennedy  pays  Dr.  L.  J.  Hammers,  $15.75  as 
payment  in  full  for  his  professional  services.  Write  a  receipt 
for  the  settlement  of  this  account. 

3.  Write  a  receipt  for  Hogan  Bros,  to  Mrs.  J.  C.  Veeder 
for  a  settlement  in  full  of  her  account  of  $11.75. 

4.  Write  a  receipt  for  Adams  Bros,  to  Mrs.  F.  R.  Fitzgerald 
for  a  settlement  in  full  of  the  account  shown  on  page  117. 

5.  Write  a  receipt  for  some  actual  payment  in  which  you 
have  been  the  receiver  of  the  money  or  have  paid  a  sum  of 
money  to  some  other  person. 

6.  I  ordered  a  suit  from  a  tailor.  He  required  a  deposit  of 
$10.00  and  gave  me  a  receipt  for  this  amount,  in  part  payment 
for  the  suit.    Write  such  a  receipt  for  a  tailor. 

7.  Write  a  receipt  to  a  plumber  from  his  employer  for 
$15.00  in  payment  for  20  hours'  work  at  75  cents  per  hour. 

The  Cash  Account 

Most  methodical  people,  whether  engaged  in  active  business 
or  not,  keep  a  cash  account  of  their  receipts  and  expenditures. 
The  cashbook  represents  the  owner's  pocketbook  or  cash 
drawer.  "Cash"  is  treated  as  a  real  person.  It  is  debited,  or 
charged  with  all  money  received;  and  is  credited  with  all  moneys 
paid  out.  Two  pages  are  usually  used  for  a  cash  account,  the 
left  hand  page  being  used  for  the  debits  and  the  right  hand  page 
being  used  for  the  credits. 

The  "Balance"  or  difference  between  the  amounts  of  the  two 
pages  will  be  the  cash  on  hand.  The  first  entry  on  each  debtor 
page  is  the  amount  of  cash  on  hand. 


136 


SEVENTH  YEAR 


Debit  Side  of  a  Boy's  Cash  Account 


Nov. 

1 

Balance  on  hand 

5 

90 

n 

3 

Errand 

25 

N 

4 

Assioting  in  Grocery  store 

1 

50 

H 

11 

M                B                    »                       If 

1 

50 

N 

18 

w           w              n                 N 

1 

50 

10 

65 

Credit  Side  of  the  Same  Boy's  Cash  Account 


Nov. 

6 

School  Supplies 

45 

H 

10 

Sweater  Vest 

2 

50 

n 

17 

School  EntertaiiiDient 

25 

n 

21 

Book 

50 

N 

30 

ToSalance 

6 

95 

10 

65 

At  the  end  of  each  month  a  cash  account  is  "balanced"  as 
shown  in  the  above  account.  This  account  shows  the  boy  to 
have  a  balance  on  hand  of  $6.95  on  Nov.  30,  because  it  takes 
that  amount  to  make  the  credit  side  of  the  account  "balance" 
the  debit  side. 

Exercise  5 

Prepare  a  cash  account  for  this  boy  during  December, 
starting  with  the  cash  on  hand  as  shown  in  the  preceding 
account  and  entering  the  following  items  on  the  proper  side 
of  the  account. 

1.  Dec.  2,  Bought,  a  necktie  50ji5;  Dec.  2,  Received  $1.50 
for  working  in  the  grocery  store;  Dec.  5,  Received  from  sale 
of  old  books  $1.15;  Dec.  9,  Received  from  the  grocery  store 
$1.50  for  services;  Dec.  14,  Bought  Christmas  present  for 
mother  $2.50;  Dec.  15,  Received  for  assistance  at  opera  house 
$1.25;  Dec.  16,  Wages  from  store  $1.50;  Dec.  19,  For  Christmas 
presents  bought  $3.85;  Dec.  23,  Wages  from  store  $1.50; 
Dec.  25,  Received  as  present  from  mother  and  father  $10.00 
in  cash;  Dec.  30,  Wages  from  store  $1.50. 


BUSINESS  FORMS  AND  ACCOUNTS  137 

2.  Balance  the  account  on  Dec.  31  and  enter  the  proper 
amount  under  "To  balance"  on  the  credit  side  of  the  account. 

3.  What  would  be  the  first  item  of  this  boy's  account  for 
January,  1917? 

The  Daybook  or  Journal 

When  goods  are  sold  on  credit,  the  merchant  enters  the  sales, 
as  they  occur,  in  an  account  book  called  the  Daybook,  or 
Journal,  stating  the  separate  items  and  the  price  of  each.  A 
single  page  of  such  an  account  book  may  contain  business 
transactions  with  various  persons. 

Where  memorandum  slips  are  kept,  many  firms  do  not  keep 
a  day  book  but  keep  these  slips  as  a  record  of  the  daily  transac- 
tions. These  memorandum  slips  are  filed  in  some  systematic 
way,  each  customer's  slips  being  kept  together. 

The  following  illustration  shows  a  typical  page  of  the  journal 
of  a  men's  clothing  store: 

135. 


1916. 

Nov.  7 

William  Smith,  Dr. 

To  3  pairs  socks  @  .25 

75 

To  1  shirt 

1  50 

To  1  necktie 

50 

To  4  collars  @  .15 

60 

To  1  pair  suspenders 

1  00 

Nov.  7 

R.  P.  Jones,  Dr. 

To  3  handkerchiefs  @  .20 

60 

To  2  union  suits  @  1.50 

3  00 

To  2  collar  buttons  @  .10 

20 

Nov.  7 

John  F.  Brown,  Cr. 
By  cash 

Nov.  7 

L.  B.  Strayer 
To  1  hat 

4  36 

3  80 
750 

460 


138  SEVENTH  YEAR 

It  will  be  seen  that  the  preposition  to  is  used  with  debits  and 
by  with  credits.  The  abbreviation  Dr.  is  used  for  debtor  and 
means  that  Wm.  Smith  and  R.  P.  Jones  are  debtors  to  the 
firm  for  the  goods  which  they  have  purchased.  The  abbre- 
viation Cr.  is  used  for  creditor  and  means  that  John  F.  Brown 
is  to  be  given  credit  on  his  account  for  the  cash  which  he  has 
paid. 

Exercise  6 

Prepare  a  page  of  a  day  book  containing  the  following 
transactions  for  Nov.  2: 

1.  Sold  J.  R.  Stock  1  pair  of  shoes  at  $5.00;  1  box  of  Hole- 
proof hose  at  $1.50;  2  collars  at  15  cents  each;  and  a  shirt  for 
$2.00. 

2.  Received  a  cash  payment  from  Wm.  Smith  for  $7.50 
to  apply  on  his  account. 

3.  Sold  Mrs.  J.  F.  Doan  1  pair  shoes  at  $6.00;  1  box  of 
Shinola  at  10  cents;  and  2  handkerchiefs  at  35  cents  each. 

4.  Add  other  accounts  that  a  general  dry-goods  and  shoe 
store  would  have.    Fill  out  the  page  in  this  way. 

Personal  Accounts 

In  a  book  called  a  ledger  a  page  or  portion  of  a  page  is  devoted 
to  transactions  with  a  single  person.  These  accounts  then  are 
called  personal  accounts  and  it  is  from  these  accounts  that  the 
monthly  statements  are  prepared. 

These  acfcounts  are  "posted"  by  a  bookkeeper  from  the 
memorandum  slips  or  daybook.  The  account  may  be  itemized 
or  the  totals  only  may  be  entered  for  each  day's  purchase. 

A  page  of  a  ledger  containing  a  personal  account  is  divided 
into  two  parts.  A  person's  indebtedness  to  the  firm  is  shown 
on  the  left  or  debtor  side  of  the  page;  and  his  payments  are 


BUSINESS  FORMS  AND  ACCOUNTS 


139 


shown  on  the  right  or  creditor  side.  This  account  is  usually 
balanced  once  a  month.  Here  is  an  account  on  the  page  of 
a  ledger: 

Dr.  Williem  Smith  Cr. 


1916 

Nov.  1 
..       7 

"     15 
«     25 

Balance  frcn>  Oct. 
ydse. 

n 
« 

7 
4 
3 
8 

50 
35 
50 
25 

1916 
Nov.  2 
"     30 

Cash 
<3<a/ance 

7 
16 

50 
10 

Sahnce 

23 

60 

23 

60 

Dec.  1 

16 

10 

The  above  personal  account  of  William  Smith  shows  a 
balance  of  $7.50  from  his  Oct.  account  still  due  the  firm. 
He  was  sent  a  monthly  statement  and  promptly  responds  on 
Nov.  2  with  a  cash  payment.  The  account  shown  in  the 
illustration  of  the  daybook  on  page  121  is  shown  here  entered 
on  the  Dr.  side  of  Wm.  Smith's  account  as  indicated  in  the 
daybook.  On  Dec.  1,  Wm.  Smith  will  be  sent  a  statement 
of  his  account,  showing  a  balance  due  of  $16.10. 


Exercise  7 

1.  Prepare  a  similar  personal  account  for  December  for 
Wm.  Smith  using  imaginary  amounts  and  balancing  his  account 
on  Dec.  31. 

2.  Prepare  a  personal  account  for  R.  P.  Jones,  including 
as  one  of  the  items,  the  account  shown  in  the  daybook  on  page 
121.     Use  imaginary  accounts  for  the  rest  of  his  account. 

3.  Prepare  a  personal  account  for  F.  W.  Trowbridge  from 
the  following  items  found  in  the  daybook:  Balance  due 
Nov.  1,  as  shown  in  ledger,  $8.75;  Nov.  3  paid  cash,  $8.75; 
Nov.  5  bought  a  hat  at  $4.00  and  a  tie  for  75  cents;  Nov.  9 
bought  1  box  of  hose  at  $1.50;  Nov.  15  bought  a  suit  for  $27.50; 
Nov.  26  bought  a  pair  of  shoes  for  $6.00;  Nov.  29  paid  cash, 
$30  00. 


140  SEVENTH  YEAR 

4.  Prepare  a  personal  account  of  a  farmer  with  a  hardware 
and  implement  company,  inserting  items  that  a  farmer  buys 
at  such  a  store. 

6.  Prepare  a  personal  account  of  a  woman  at  a  druggist's, 
showing  purchases  of  various  medicines,  spices,  and  other 
supplies  which  a  drug  store  in  your  community  keeps. 

The  Inventory 

An  inventory  consists  of  a  list  of  articles  on  hand  at  the  time 
the  inventory  is  taken  together  with  a  statement  of  the  value 
of  the  various  articles.  An  inventory  is  a  necessity  for  a  firm 
in  estimating  the  amount  of  gain  or  loss  in  their  business. 

Inventory  of  a  School  Recitation  Room 

Furniture: 

1  teacher's  desk $15 .  00 

25  single  desks  at  3.50 87. 50 

2  chairs  at  2.00 4.00 

1  filing  cabinet 20. 00 

1  desk  book  rack 1 .  25 


Supplies : 

2  sets  practice  exercises  in  arithmetic $19. 20 

1  ream  white  practice  paper 48 

1  hektograph  (2  faces) 2 .  50 

3  arithmetic  texts  (Chadsey-Smith) 1.92 

2  boxes  crayon  at  20  cents , 40 


Pictures  and  Flowers: 

2  window  boxes  of  ferns  at  5.00 $10. 00 

1  picture 10. 00 


Total  value . 


BUSINESS  FORMS  AND  ACCOUNTS  141 

When  there  has  been  a  loss  of  household  goods  by  fire, 
insurance  companies  usually  demand  that  an  inventory  be 
made  of  the  goods  destroyed  by  fire.  It  is  therefore  a  good 
policy  to  make  out  an  inventory  of  your  household  goods  at 
the  cost  price  and  keep  it  in  a  safe  place  for  reference  in  case 
of  the  destruction  of  your  goods  by  fire. 

Exercise  8 

1.  With  the  help  of  the  teacher  and  a  supply  catalogue, 
make  out  an  inventory  of  the  supplies  and  furniture  in  your 
school  room.  This  may  be  presented  to  the  school  board  for 
reference  in  case  of  fire. 

2.  Make  an  inventory  of  the  furniture  and  furnishings  in 
your  home,  estimating  the  goods  at  cost  and  give  this  to  your 
parents  to  deposit  in  the  safety  deposit  box  in  the  bank  for 
reference  if  it  were  needed  in  making  out  an  inventory  in  case 
of  fire. 

3.  If  your  father  is  on  a  farm  or  in  a  business  in  the  city, 
assist  him  in  making  out  an  inventory  for  his  supplies  that  he 
has  on  hand. 

4.  Make  an  inventory  of  your  own  school  supplies. 

The  Pay  Roll 

In  factories,  stores,  and  offices  where  the  employees  are 
paid  by  the  hour,  there  must  be  some  system  for  keeping  a 
record  of  their  time.  Some  firms  employ  a  card  system  on 
which  each  employee  has  his  time  checked  when  he  begins 
and  leaves.  Others  use  a  system  of  checks,  the  worker  taking 
out  his  check  when  he  begins  and  returning  it  when  he  leaves. 
Some  employers  have  an  electric  clock  with  various  numbers, 
each  laborer  punching  his  number  on  entering  and  also  on  leav- 
ing. The  record  is  made  on  a  revolving  sheet  of  paper  on  the 
proper  time  space. 


142 


SEVENTH  YEAR 


The  following  form  is  a  simple  arrangement  for  making  out 
the  pay  roll: 


NO. 

Nana 

I'on. 

TUOE, 

Wed. 

Thurs . 

m. 

Snt. 

TotBl 

Tine 

Rate 
per  hr. 

Arounl 
Due 

1, 

A 

Brom! 

8 

8 

9 

8 

10 

6 

49 

zv 

vl2.25 

2. 

s. 

Jor.4!< 

8 

8 

9 

8 

9 

9 

51 

25X 

12.75 

3. 

J 

Echiridt 

9 

8 

8 

9 

9 

8 

35^ 

♦  . 

F 

JbnB«n 

9 

9 

7 

8 

9 

9 

3bf 

5. 

P 

Crtiijory 

B 

8 

8 

8 

10 

6 

40i< 

ft. 

R 

Dersey 

7 

8 

9 

9 

8 

6 

40|* 

7, 

S. 

Stcddfrd 

9 

9 

9 

9 

10 

6 

32/ 

8. 

V. 

Strlpri 

9 

9 

8 

8 

9 

8 

36(< 

9. 

N. 

Costollo 

8 

e 

8 

8 

8 

8 

30i« 

The  amount  of  time  is  multiplied  by  the  proper  rate  per  hour 
for  each  employee  and  the  various  sums  placed  in  the  last 
column  showing  the  amount  due.  From  this  pay  roll  the 
cashier  makes  out  a  memorandum  showing  the  number  of 
each  kind  of  bills  and  each  kind  of  coin  in  order  to  put  the 
exact  amount  in  each  employee's  envelope,  to  be  handed  to 
him  at  the  close  of  the  week.  The  following  form  gives  one 
plan  for  the  cashier's  memorandum : 


Cashier's 

5  Memorandum 

No. 

Wd^es 

*20 

*I0 

^5 

^^2 

*i 

SO-^ 

254^ 

10* 

54^ 

1<^ 

1 

/:i2S 

/ 

/ 

/ 

2 

i2.7S 

/ 

/ 

/ 

/ 

3 

4 

5 

6 

7 

8 

9 

TML 

? 

? 

? 

? 

? 

? 

? 

? 

? 

? 

r> 

BUSINESS  FORMS  AND  ACCOUNTS  143 

Exercise  9 

1.  Complete  the  rest  of  the  pay  roll  as  indicated  in  the  por- 
tions already  filled  out. 

2.  Fill  out  the  rest  of  the  cashier's  memorandum  in  the 
manner  shown  in  the  first  two  lines. 

3.  Find  the  total  number  of  each  denomination  of  bills  and 
coins. 

4.  What  is  the  total  amount  of  wages  due  the  employees? 

6.  From  the  number  of  bills  and  coins  in  each  column,  see 
if  the  cashier's  memorandum  checks  with  the  total  amount  in 
wages. 

Exercise  10.    Review 

1.  Why  should  a  customer  keep  a  memorandum  or  sales- 
man's shp  for  grocery  orders? 

2.  What  is  an  invoice  or  bill?  When  are  invoices  used  in- 
stead of  a  salesman's  slip? 

3.  Give  5  things  which  a  receipt  should  show. 

4.  What  is  the  advantage  of  paying  an  account  with  a  check 
in  case  no  receipt  is  issued? 

6.  What  items  go  on  the  debit  side  of  a  cash  account?  What 
items  are  put  on  the  credit  side  of  the  account? 

6.  What  is  the  balance  in  a  cash  account? 

7.  What  is  the  use  of  the  daybook? 

8.  Into  what  accoimt  books  are  the  items  of  the  daybook 
transferred? 

9.  Describe  a  personal  account. 

10.  Why  should  every  householder  have  an  inventory  of  his 
household  goods? 


lU 


SEVENTH  YEAR 


PARCEL  POST 

Merchandise  is  shipped  by  the  post  ofRce  department  under 
a  system  of  parcel  post  rates.  These  rates  vary  according  to 
the  weight  and  the  distance  they  are  carried.  For  convenience 
in  handling  the  matter  of  distance  the  government  has  estab- 
lished a  system  of  zones.     See  the  following  table  for  rates: 


Weight  of 
Parc»l 

Local 
Zona 

Zones  1  ft  2 

Zona  3 

Zone  4 

Zone  5 

Cities  not 
Dore  than  150 
miles  distant 

Cities  151 

to  300  miles 

distant . 

Cities  301 

to  6C0  mil^s 

distant . 

Cities  601 

to  1000  miles 

distant. 

Over  4  et . 

up 

to  1  lb. 

5i« 

5« 

6j( 

7fS 

8« 

"      1  lb. 

» 

-    2  lb. 

6* 

6f 

8iS 

11(« 

14i« 

"      2  lb. 

- 

"    3  lb. 

6* 

■'f 

10(« 

15i2 

20;i 

"      3  lb. 

• 

"    4  lb. 

1* 

8fl 

12K 

19K 

26;* 

»     4  lb. 

- 

"    5  lb. 

1* 

9« 

14i< 

23,< 

32i« 

"    10  lb. 

•• 

"11   lb. 

10^ 

15« 

26(« 

47i« 

esf 

"    15  lb. 

" 

"16  lb. 

13« 

20iJ 

36(t 

67i« 

9B^ 

"    19  lb. 

" 

"20  lb. 

15(S 

24j! 

44i« 

83^                £1.22 

"    25  lb. 

- 

••26  lb. 

18^ 

30« 

50  pounds      the  limit  in  weitht 
for  parcels  in  the  local  zone  and 
zones  1  and  2. 

20  pounds  is  the  limit  in  weight 
for  the  other  zones. 

"    30  lb. 

" 

"31  lb. 

20(f 

35i« 

"    40  lb. 

" 

"41  lb. 

25(« 

45i« 

•    49  lb. 

m 

"50  lb. 

30^ 

M« 

eluded  in  t 
lack  of  spa 

/    ana  s 
his  table  on 
ce. 

are  not  in- 
accouut  of 

Exercise  11 

1.  A  farmer  101  miles  from  Chicago  wishes  to  ship  a  package 
of  butter  weighing  4 1  pounds  to  a  customer  in  that  city. 
Find  the  parcel  post  charges  on  the  shipment. 

2.  The  distance  from  Pittsburgh  to  Chicago  is  492  miles. 
How  much  will  it  cost  to  send  a  4-pound  package  from  Chicago 
to  Pittsburgh  by  parcel  post? 

3.  The  distance  from  St.  Louis  to  New  Orleans  is  748  miles. 
How  much  will  it  cost  to  ship  a  10§-pound  package  by  parcel 
post  from  New  Orleans  to  St.  Louis? 


BUSINESS  FORMS  AND  ACCOUNTS  145 

4.  The  distance  from  Detroit  to  New  York  is  595  miles. 
How  much  will  a  parcel  post  shipment  of  15  f  pounds  cost 
between  those  cities? 

5.  I  wish  to  ship  a  package  of  merchandise  weighing  4^ 
pounds  to  a  city  in  the  third  zone.  How  much  postage  must 
I  put  on  the  package? 

6.  A  man  in  southern  Wisconsin  advertised  a  12-pound 
case  of  fancy  comb  honey  for  $3.60  per  case,  charges  prepaid. 
How  much  more  would  it  cost  him  to  ship  to  a  customer  in 
the  third  zone  than  to  one  in  the  second  zone? 

7.  A  farmer  agreed  to  supply  a  city  customer  with  2  pounds 
of  butter  per  week  at  52  cents  per  pound,  the  customer  paying 
the  parcel  post  charges.  The  city  was  in  the  first  zone.  How 
much  will  the  customer  save  in  a  year  if  he  has  his  butter 
shipped  in  4^-pound  packages  every  two  weeks  instead  of 
2^-pound  packages  every  week? 


Find  the  parcel  post  charges  on  the  following  parcel  post 

packages: 

Weight 

Zone                                            Charges 

8.  8  ounces 

Fourth                                         ? 

9.  3  pounds 

Fifth                                        ? 

10.  15^  pounds 

Third                                       ? 

11.  50  pounds 

Second                                      ? 

12.  20  pounds 

Fourth                                      ? 

13.  10  J  pounds 

Third                                        ? 

14.  5  pounds 

Fifth                                         ? 

15.  3^  pounds 

Fourth                                      ? 

16.  2  pounds 

Fifth                                         ? 

17.  11  pounds 

Third                                        ? 

18.  31  pounds 

Second                                      ? 

19.  40  pounds 

First                                         ? 

20.  19  J  pounds 

Fourth                                      ? 

146  SEVENTH  YEAR 

Freight  Rates 

Railroad  companies  figure  freight  rates  to  the  large  cities 
and  make  practically  the  same  rates  to  the  smaller  cities  in  the 
vicinity  of  each  large  city.  Merchandise  is  divided  for  freight 
shipments  into  four  classes.  Among  the  various  articles  hsted 
in  each  class  are: 

(1)  First  class — Books,  clocks,  dry  goods,  fire  arms,  lamps, 
rugs,  toys,  etc. 

(2)  Second  class — Bedsteads,  cream  separators,  extension 
tables,  hnoleum,  refrigerators,  wheelbarrows,  etc. 

(3)  Third  class — Iron  kettles,  iron  safes,  stoves  and  ranges, 
etc. 

(4)  Fourth  class — Anvils,  poultry  food,  steel  roofing,  stock 
food,  plain  or  barbed  wire,  etc. 

Express  Rates 

Express  rates  vary  with  the  weight  of  the  shipment  and  the 
distance  between  the  shipping  points.  Express  rates  are  higher 
than  freight  rates,  but  they  include  the  delivery  of  the  package, 
while  freight  is  dehvered  at  the  expense  of  the  person  receiving  it. 

Express  and  freight  rates  between  any  two  cities  may  be 
obtained  by  asking  the  agents  at  the  express  and  freight  offices. 

Exercise  12 

1.  The  freight  rates  between  two  cities  are:  1st  class  $.82 
per  cwt.;  2nd  class  $.68;  3rd  class  $.53;  and  4th  class  $.43. 
Find  the  cost  of  the  freight  between  these  two  cities  on  a  box 
of  books  weighing  100  pounds;  on  a  stove  weighing  675  pounds; 
on  320  pounds  of  barbed  wire. 

2.  The  express  rate  between  two  cities  if  $1.26  per  hundred 
pounds.  Find  the  express  on  a  box  of  dry  goods  weighing  240 
pounds. 

8.  The  express  rate  between  two  cities  is  $1.81.  What  will 
be  the  express  charges  on  a  barrel  of  apples  weighing  160  pounds? 


CHAPTER  VI 


PRACTICAL  MEASUREMENTS 

As  a  proper  preparation  for  the  problems  in  practical  measure- 
ments a  review  of  the  following  facts  is  essential. 

Refer  to  the  tables  in  the  back  of  the  book  to  recall  facts 
that  you  have  forgotten.  You  will  need  these  facts  in  solving 
problems  in  daily  life. 

Exercise  1 

20.  1  rod  =  ?  feet. 

21.  1  common  year  =  ?  days. 

22.  1  leap  year  =  ?  days. 

23.  1  mile  =  ?  feet. 

24.  1  peck  =  ?  quarts. 

25.  1  bushel  =  ?  cu.  in. 

26.  1  gross  =  ?  dozen. 

27.  1  cord  =  ?  cu.  ft. 

28.  1  gallon =?  quarts. 

29.  1  bushel  =  ?  pecks. 

30.  1  mile  =  ?  rods. 

31.  1  gross  =  ?  things. 

32.  1  bushel  =  ?  quarts. 

33.  1  acre  =  ?  sq.  rd. 

34.  1  mile  =  ?  yards. 
36.  1  cu.  foot  =  ?  gal.  (approx.) 

36.  1  square  mile  =  ?  acres. 

37.  1  square  rod  =  ?  sq.  yd 

38.  1  barrel  =  ?  gallons. 


1.  1  yard  =  ?  feet. 

2.  1  pound  =  ?  ounces. 

3.  1  minute  =  ?  seconds. 

4.  1  foot  =  ?  inches. 

5.  1  square  yard  =  ?  sq.  ft 

6.  1  dozen  =  ?  things. 

7.  1  square  foot  =  ?  sq.  in. 

8.  1  ton  =  ?lb. 

9.  1  long  ton  =  ?  lb. 

10.  1  gallon =?  cu.  in. 

11.  1  cubic  yard  =  ?  cu.  ft. 

12.  1  week  =  ?  days. 

13.  1  yard  =  ?  inches. 

14.  1  quire  =  ?  sheets. 

15.  1  hour  =  ?  minutes. 

16.  1  cubic  foot  =  ?  cu.  in. 

17.  1  ream  =  ?  sheets. 

18.  1  quart  =  ?  pints. 

19.  1  day  =  ?  hours. 


147 


148  SEVENTH  YEAR 

Exercise  2.    Miscellaneous  Problems 

1.  How  many  dozen  eggs  are  there  in  a  standard  crate 
containing  360  eggs? 

2.  How  many  square  feet  are  there  in  an  acre? 

3.  How  many  cubic  inches  are  there  in  a  quart,  liquid 
measure? 

4.  How  many  cubic  inches  are  there  in  a  quart,  dry  measure? 

5.  How  many  inches  are  there  in  a  mile? 

6.  The  capacity  of  a  coal  car  is  70,000  pounds.  How  many 
long  tons  of  coal  will  it  hold? 

7.  A  pile  of  cord  wood  is  20  feet  long  and  6  feet  high.  If 
the  sticks  are  4  feet  long,  how  many  cords  does  the  pile  contain? 

8.  If  round  steak  is  selling  at  24  (if  a  pound,  how  much 
should  a  butcher  charge  you  if  the  scale  reads  1  lb.  12  oz.? 

9.  A  lot  is  165  feet  long  and  65  feet  wide.  Express  the 
dimensions  of  the  lot  in  rods.  How  many  feet  of  fence  will  it 
take  to  enclose  the  lot? 

10.  A  horse  is  16  hands  high.    (A  hand  is  4  in.)    How  high 
is  the  horse? '  (Express  height  in  feet  and  inches.) 

Exercise  3 

Tell  what  the  following  numbers  stand  for: 

Example:     1.  36  in.  =  the  number  of  inches  in  a  yard. 

2.  231  cu.  in.  7.  27  cu.  ft.  12.  24  sheets  17.  1728  cu.  in. 

3.  160sq.  rd.  8.  144  sq.in.  13.  2000  lb.  18.  7  days 

4.  5280  ft.  9.  16|  ft.       14.  30i  sq.  yd.  19.  128  cu.  ft. 

5.  4  qt.  10.  12  in.         15.  5  J  yd.  20.  365  days 

6.  2150.42  cu.  in.  11.  320  rd.      16.  9  sq.  ft.  21.  1760  yd. 


PRACTICAL  MEASUREMENTS— ANGLES        149 

The  following  figures  and  definitions  are  very  important 
because  they  are  used  in  describing  the  various  kinds  of  figures 
in  measurements,  both  in  this  book  and  in  their  applications  in 
daily  life. 


A  Straight  Line 


-B 


A  straight  line  is  a  line  which  does  not  change  its  direction 
at  any  point.  Two  letters,  one  at  each  end  of  the  line,  are 
generally  used  to  name  a  line — as  the  line  A  B. 

Parallel  Lines 


Figure  1 


Figure    2 


Figure  3 


If  two  straight  lines  on  a  flat  surface  are  always  the  same 
distance  apart  and  therefore  can  not  meet,  no  matter  how 
far  they  are  extended,  they  are  said  to  be  parallel.  (See  Figures 
1,  2  and  3.) 

The  rails  on  a  straight  stretch  of  a  railroad  track  are  parallel 
because  they  are  the  same  distance  apart.  Give  another 
example  of  parallel  lines. 


Figure  4 


Figure  6 


150 


SEVENTH  YEAR 


When  two  lines  meet,  they  form  an  angle.  The  size  of  the 
angle  depends  upon  the  difference  in  direction  of  the  lines  and 
not  upon  the  length  of  the  lines  forming  the  angle.  For  example, 
the  angles  in  Figures  4  and  5  are  equal. 

The  point  A  where  the  two  lines  meet  is  called  the  vertex  of 
the  angle. 

The  angle  in  Figure  4  may  be  read  angle  A  or  angle  B  A  C  or 
angle  1.  For  shortness  the  sign  <  is  used  for  the  word  angle. 
Angle  A  is  the  same  as  <  A. 


D 


1 


C 
Figure  6 


Figure  7 


If  a  straight  line  is  drawn  to  meet  another  straight  line,  so 
that  the  angles  thus  formed  (as  angles  1  and  2  in  Figure  6) 
are  equal,  the  lines  are  -perpendicular  to  each  other.  ^ 

Perpendicular  lines  form  right  angles. 

An  angle  smaller  than  a  right  angle  is  an  axyute  angle. 

An  angle  larger  than  a  right  angle  is  an  obtuse  angle. 

Angles  1  and  2  in  Figure  6  are  right  angles.  Angle  2  in 
Figure  7  is  an  acute  angle  and  Angle  1  in  Figure  7  is  an  obtuse 
angle. 

^Right  angles  may  be  formed  by  paper  folding.  Take  a  sheet  of  paper 
and  fold  an  edge  over  on  ItseK.  Then  crease  with  the  edges  held  together. 
The  crease  will  be  perpendicular  to  the  edge  of  the  paper.  Show  how  to 
fold  the  paper  to  make  acute  and  obtuse  angles. 


PRACTICAL  MEASUREMENTS— RECTANGLES  151 


:::P 


m 


Rectangles 
A  figure  of  four  sides  is  a  quadrilateral. 

How  many  sides  has  the  rectangle 
A  B  CD? 

How  are  the  two  pairs  of  opposite  sides 
drawn? 

How  many  angles  has  a  rectangle? 

What  kind  of  angles  are  they? 

A  rectangle  is  a  quadrilateral  whose 
opposite  sides  are  parallel  and  whose  angles  are  right  angles. 


Exercise  4 

1.  How  many  small  squares  are  there  in  one  row  along  the 
base  A  B? 

2.  How  many  rows  are  there  in  the  width  or  altitude,  B  C  ? 

3.  How  many  small  squares  are  there  in  the  area  of  the 
rectangle  A  B  CD? 

We  see,  then,  that  the  area  of  a  rectangle  may  be  found  by 
multiplying  1  square  unit  of  area  by  the  number  of  units  in 
length  by  the  number  of  the  same  kind  of  units  in  the  width. 

We  can  state  this  more  briefly  in  the: 

PRINCIPLE:    The  area  of  a  rectangle  is  equal  to  the  product 
of  the  base  and  altitude. 

4.  Let  A  stand  for  the  area,  b  for  the  base  and  a  for  the 
altitude.  The  above  principle  can  be  stated  in  a  much  shorter 
form,  called  a  formula:^    A  =  b  X  a. 

6.  If  b  and  a  are  given,  how  do  you  find  the  area,  A? 

6.  If  the  area,  A,  and  the  base,  b,  are  given,  how  do  you 

find  the  altitude,  a? 

'Show  that  the  letters  are  used  in  a  formula  to  stand  for  a  word  in  order 
that  time  may  be  saved  when  the  principle  needs  to  be  stated  in  writing. 


152  SEVENTH  YEAR 

7.  If  the  area,  A,  and  the  altitude,  a,  are  given,  how  do  you 
find  the  base,  b? 

The  perimeter  of  a  rectangle  is  equal  to  the  sum  of  its  four  sides. 

Exercise  5 

1.  If  the  base  A  B  is  15  inches  and  the  altitude  B  C  is  8 
inches,  what  is  the  perimeter  of  the  rectangle  A  B  C  D  ? 

2.  What  is  the  area  in  square  feet  of  the  floor  of  your 
recitation  room?^ 

5.  What  is  the  perimeter  in  feet  of  this  room? 

4.  How  much  would  it  cost  to  put  a  baseboard  around  the 
sides  of  the  room  at  10  cents  per  running  foot?  Make  allow- 
ances for  the  doors. 

6.  How  many  board  feet  of  lumber  were  used  in  covering 
this  floor  if  an  allowance  of  J  of  the  area  is  added  to  cover 
loss  from  cutting  and  the  amount  used  in  tongue  and  groove 
work  on  the  boards? 

6.  What  did  this  lumber  cost  at  $80  per  M? 

7.  In  a  certain  park  there  is  a  rectangular  wading  pool 
40  feet  long,  28  feet  wide  and  2  feet  deep.  How  much  did  it 
cost  to  cement  the  bottom  and  sides  of  this  pool  at  15  cents 
per  square  foot? 

8.  Around  the  outside  of  the  pool  there  is  a  concrete  walk 
3  feet  wide.    Find  the  area  of  the  concrete  walk. 

9.  What  is  the  perimeter  of  the  pool?  What  is  the  perimeter 
of  the  walk? 

10.  A  rectangular  field  is  80  rods  long  and  40  rods  wide. 
How  many  acres  are  there  in  the  field? 

Problems  using  local  data  should  be  prepared  by  the  pupils  and  presented 
to  the  class  for  solution. 


PRACTICAL  MEASUREMENTS— PROBLEMS     153 

11.  What  must  be  the  dimensions  of  a  rug  for  a  room  18 
feet  in  length  and  14  feet  in  width,  if  a  yard  of  uncovered  floor 
space  is  left  on  each  end  of  the  room  and  2^  feet  is  left  on  each 
side? 

12.  How  many  square  feet  of  floor  space  will  be  left  uncovered 
in  the  room?     Show  two  ways  of  solving  this  problem. 

13.  A  rectangular  lot  contains  9570  square  feet.  It  is  130 
feet  long.    How  wide  is  it? 

14.  Find  the  cost  of  covering  the  blackboard  space  in  your 
school  room  with  slate  at  15izl  a  square. foot. 

16.  How  much  will  it  cost  to  cover  the  floor  of  a  kitchen 
9'xl5'  with  linoleum  at  $1.75  per  square  yard? 

16.  For  a  room  to  be  properly  lighted,  the  area  of  the  glass 
surface  should  be  at  least  ^  of  the  area  of  the  floor  space.  Is 
your  school  room  properly  lighted? 

17.  A  field  is  80  rods  long.  How  many  rows  of  com  will  it 
take  to  make  an  acre  if  the  rows  are  3  feet  8  inches  apart? 

18.  A  rectangular  field  contains  60  acres.  It  is  120  rods 
long.     How  wide  is  it? 

19.  How  long  is  a  tennis  court?  How  wide  is  it  for  doubles? 
How  many  square  feet  does  it  contain? 

20.  A  township  is  6  miles  long  and  6  miles  wide.  How  many 
acres  are  there  in  a  township? 

21.  A  mile  of  a  certain  city  street  is  to  be  paved  with  brick 
at  a  cost  of  $1.20  per  square  yard.  If  the  pavement  is  to  be 
30  feet  wide,  what  will  be  the  cost  per  mile? 

22.  The  property  owners  are  required  to  pay  for  half  of  the 

width  of  the  pavement  extending  in  front  of  their  lots.^     How 

much  would  the  pavement  cost  in  front  of  a  lot  50  feet  wide? 

'The  city  usually  pays  for  the  cost  of  the  pavement  at  the  intersections 
of  the  street. 


154 


SEVENTH  YEAR 


Boy  Scouts'  Tents 

Boy  Scouts  are  taught  to  make  tents  out  of  square  and 
rectangular  pieces  of  canvas.  The  figures  below  show  how  to 
make  a  tent  out  of  square  sheets  of  canvas.  A  square  7  feet 
by  7  feet  will  provide  a  shelter  for  1  man  and  a  square  9  feet 
by  9  feet  a  shelter  for  two  men. 


The  following  figures  show  how  to  make  a  tent  from  a 
rectangular  piece  of  canvas  twice  as  long  as  it  is  wide.  See  if 
you  can  hang  and  stake  such  a  tent  properly. 


Camping 

Among  the  various  requirements  necessary  to  obtain  a  merit 
badge  for  Camping,  a  scout  must: 

1.  Have  slept  fifty  nights  in  the  open  or  under  canvas  at 
different  times. 

2.  Demonstrate  how  to  put  up  a  tent  and  ditch  it. 
(From  the  Handbook  for  Boys — The  Boy  Scouts  of  America.) 


PRACTICAL  MEASUREMENTS— BOY  SCOUTS   155 

Exercise  6 

1.  How  many  square  feet  of  canvas  are  needed  in  a  one-man 
shelter  that  is  made  from  a  sheet  7'x7'? 

2.  How  many  square  feet  of  canvas  are  there  in  ai  two-man 
shelter? 

3.  Two  Boy  Scouts  found  that  they  could  buy  7'x7'  sheets 
of  ducking  for  $1.75  each  or  a  9'x9'  sheet  for  $2.50.  Which 
would  provide  the  cheaper  shelter  for  them,  the  single  or  the 
double  tents? 

4.  Four  Boy  Scouts  found  that  they  could  buy  a  canvas 
9'xl8'  for  $4.75.  How  much  would  they  save  by  buying  this 
sheet  and  making  a  four-man  shelter,  rather  than  buying 
individual  sheets  costing  $1.75  each? 

Gardening 

Among  the  various  things  that  a  scout  may  do  to  obtain  a 
merit  badge  for  gardening  is : 

(a)  To  operate  a  garden  plot  of  not  less  than  20  feet  square 
and  show  a  net  profit  of  not  less  than  $5  on  the  season's 
work.     Keep  an  accurate  crop  report. 

Exercise  7 

1.  If  the  garden  plot  must  be  at  least  20  feet  square,  how 
many  square  feet  does  this  minimum  sized  plot  contain? 

2.  Express  the  area  of  the  minimum  plot  in  square  rods. 

3.  What  part  of  an  acre  is  this  minimum  plot? 

4.  A  certain  boy  raised  beans  on  a  garden  plot  33  feet  wide 
and  132  feet  long.  His  profit  was  $110.75.  Find  his  profit  per 
square  rod.  Would  he  have  been  able  to  secure  the  merit 
badge  for  gardening  on  a  minimum  sized  plot  at  that  rate? 

6.  What  would  have  been  his  profit  per  acre  at  that  rate? 


156  SEVENTH  YEAR 

Parallelograms 

A  parallelogram  is  a 
quadrilateral  with  its  oppo- 
site sides  parallel.  The 
figure  on  the  left  is  a 
parallelogram. 

A  rectangle  is  a  parallelogram  with  its  angles  all  right  angles. 
A  parallelogram  with  angles  not  right  angles  is  called  a  rhomboid. 
The  figure  above  is  likewise  a  rhomboid. 

^ ■$.        The  line  A  B  is  called 

A  /'*     *^^  ^^^^  ^^  *^^  parallelo- 

/  I  /   I     gram.    The  line  D  E,  which 

/     i  /     \     is    the    perpendicular    dis- 

A       E  BO     tance    between    the    base 

D  C  and  the  base  A  B,  is  called  the  altitude  of  the  parallelogram. 

Cut  out  of  a  sheet  of  paper  a  parallelogram  similar  to 
A  B  C  D,  Fold  over  the  edge  A  E  on  the  base  A  B  and  crease 
along  the  line  D  E.  Cut  or  tear  off  the  part  A  E  D  and  fit 
it  in  the  position  B  O  C.    What  shape  is  the  figure  D  E  O  C? 

Show  that  the  rectangle  D  E  O  C  has  the  same  base  and 
altitude  as  the  parallelogram  A  B  C  D. 

Cut  out  a  parallelogram  with  a  base  of  6  inches  and  an 
altitude  of  3  inches.  Change  into  a  rectangle  with  the  same 
base  and  altitude.  What  is  the  area  of  this  rectangle?  Since 
the  same  amount  of  paper  forms  the  parallelogram,  what  is 
the  area  of  the  parallelogram? 

Then  show  how  we  obtain  the  principle:  The  area  of  a 
parallelogram  is  equal  to  the  product  of  its  base  times  its 
altitude. 

This  principle  may  also  be  expressed  by  the  formula: 

A  =  b  X  a. 
In  this  formula  what  is  the  product  and  what  are  the  factors? 


PRACTICAL  MEASUREMENTS— PROBLEMS    157 

Exercise  8 

1.  If  the  base  and  altitude  of  a  parallelogram  are  given,  how 
do  you  find  the  area,  A?^ 

2.  If  the  area,  A,  and  the  base,  b,  of  a  parallelogram  are 
given,  how  do  you  find  the  altitude,  a? 

3.  If  the  area.  A,  and  the  altitude,  a,  of  a  parallelogram  are 
given,  how  do  you  find  the  base,  b? 

4.  The  base  of  a  parallelogram  is  4  feet  and  the  altitude  is 
3  feet.    What  is  its  area? 

6.  The  area  of  a  parallelogram  is  24  square  feet.  The 
altitude  of  the  parallelogram  is  4  feet.     Find  the  base. 

6.  Find  the  area  of  a  parallelogram  with  a  base  of  7  feet 
and  an  altitude  of  2  yards. 

7.  A  flower  bed  is  shaped  in  the  form  of  a  parallelogram 
with  each  side  equal  to  6  feet.  By  measuring  I  find  the  per- 
pendicular distance  between  the  sides  to  be  3^  feet-  What 
is  the  area  of  the  flower  bed? 

8.  What  is  the  perimeter  of  the  flower  bed  described  in 
the  preceding  problem? 

9.  How  many  bricks  8  inches  long  would  it  take  to  build  a 
border  one  brick  thick  around  this  flower  bed? 

10.  The  area  of  a  field  in  the  form  of  a  parallelogram  is  20 
acres.  The  base  is  80  rods.  What  is  the  perpendicular  distance 
between  the  bases  (the  altitude)? 

Fill  in  the  missing  dimensions: 

Aba 

11.  400  sq,  ft.  25  ft.  ? 

12.  ?  5  yd.  12  ft. 

13.  36  sq.  yd.  9  yd.  ? 

'Such  problems  as  1  to  3  of  this  exercise  give  practice  in  reviewing  the 
principles  relating  to  product  and  factors.  Have  pupils  state  the  answers 
in  formulae  if  possible. 


158  SEVENTH  YEAR 

c       F  Trapezoids 

\2/  A  trapezoid  is  a  quadrilateral 

\aj         with  only  one  pair  of  opposite 
A  sides  parallel. 

/  ^  \  The  figure  A  B  C  D  is  a  trape- 

^       *       zoid. 

1.  By  measuring  find  the  middle  point  O  of  the  line  C  B. 
Draw  E  F  parallel  to  the  line  A  D.  By  cutting  off  part  E  B  O 
and  placing  it  in  the  position  O  F  C,  what  shaped  figure  is 
formed? 

2.  If  A  B  =  16  inches  and  D  C  =  12  inches,  what  is  the 
length  of  A  E? 

By  using  other  numbers  and  remembering  that  E  B  is  the 
same  length  as  C  F,  you  can  show  that  the  base  of  the  parallelo- 
gram into  which  the  trapezoid  has  been  changed  is  ^  the  sum 
of  the  two  bases  of  the  trapezoid.  The  altitude  of  the  parallelo- 
gram is  the  same  as  the  altitude  of  the  trapezoid.  With  this 
information  show  that: 

PRINCIPLE:    The  area  of  a  trapezoid  is  equal  to  half  the  sum 
of  the  two  bases  times  the  altitude. 

Exercise  9 

1.  Find  the  area  of  a  trapezoid  whose  bases  are  12  inches 
and  18  inches  and  whose  altitude  is  11  inches. 

Solution:     §  of  (12+18)  =  15,  number  of  inches  in  §  the 

sum  of  the  bases. 
11X15  =  165. 
Therefore:    The  area  of  the  trapezoid  is  165  square  inches. 

2.  Find  the  area  of  a  trapezoid  of  which  the  upper  base  is 
10  feet,  and  the  lower  base  18  feet  and  the  altitude  9  feet. 

3.  A  board  is  10  inches  wide  at  one  end  and  14  inches  wide 
at  the  other  end.  If  it  is  10  feet  long,  how  many  square  feet 
are  there  on  the  surface  of  the  board? 


PRACTICAL  MEASUREMENTS— TRIANGLES    159 


20  -RDS. 


to  RD5. 


4.  A  man  once  gave  me  this  problem  to 
solve.  A  railroad  cut  off  a  small  piece 
of  his  land  in  the  form  shown  at  the  left. 
He  had  threshed  oats  off  of  the  tract  and 
wished  to  compute  the  yield  per  acre, 
but  he  did  not  know  how  many  acres 
there  were  in  the  piece.  Find  the  number 
of  acres  in  the  field. 

6.  If  the  field  yielded  210  bushels  of 
oats,  what  was  the  average  yield  per  acre? 


Triangles 

A  triangle  is  a  figure  bounded  by  three  straight  lines,  called 
its  sides.     As  the  name  indicates,  a  fn'-angle  has  three  angles. 

Triangles  may  be  grouped  according  to  sides  or  angles. 

(Scalene — no  two  sides  being  equal. 

1.  Sides   <  Isosceles — having  only  two  sides  equal. 

[Equilateral — having  all  three  sides  equal. 

(Acute  Angled — having  all  the  angles  acute. 

2.  An.g\es<Ohtuse  Angled — having  one  angle  obtuse. 

[Right  Angled — having  one  angle  a  right  angle. 


Scalene 


Isosceles 


Equilateral 


Acute  Angled 


Obtuse  Angled 


Right  Angled 


160  SEVENTH  YEAR 

Areas  of  Triangles 

The  altitude  of  any  triangle 

C^^.....-.........— T       is   the   perpendicular   from   the 

/ijj^N.  /        vertex  to  the  base,  as  the  line 

I  '^  ^s.       ;  Draw  any  shaped  triangle  as 

H ^B  ABC. 

From  C   draw    a   line    C    D 
parallel  to  the  base  of  the  triangle,  A  B. 

From  B  draw  a  line  parallel  to  the  side  A  C. 

What  kind  of  figure  is  A  B  D  C?  How  does  its  base  and 
altitude  compare  with  the  base  and  altitude  of  the  triangle 
ABC? 

Cut  out  your  parallelogram  and  cut  it  along  the  diagonal 
line  B  C.    How  do  triangles  ABC  and  B  D  C  compare  in  size? 

The  triangle  A  B  C  is  what  part  of  the  parallelogr9,m  A  B  D  C? 

The  area  of  the  parallelogram  =  the  product  of  base  X  altitude. 

The  area  of  the  triangle  =  §  the  area  of  the  parallelogram. 

Show  that  the  areas  of  the  other  forms  of  triangles  equal 
§  the  area  of  the  parallelograms  constructed  as  shown  in  the  ■ 
scalene  triangle  above. 

PRINCIPLE :   The  area  of  any  triangle  is  one-half  of  the  product 
of  the  base  times  the  altitude. 

Draw  a  triangle  on  a  sheet  of  paper.  Cut  it  out  carefully 
and  number  the  angles  1,  2  and  3.  Cut  the  triangle  into  three 
parts  so  that  you  can  arrange  the  angles  about  a  point  on  one 
side  of  a  straight  line.  Show  that  the  sum  of  the  three  angles  of  a 
triangle  is  equal  to  two  right  angles  (or  180°).  Draw  other 
shaped  triangles  to  show  that  this  principle  holds  true  for  any 
shaped  triangle. 


PRACTICAL  MEASUREMENTS— TRIANGLES     161 

Exercise  10 

1.  The  base  of  a  triangle  is  16  inches  and  the  altitude  is 
11  inches.     Find  the  area. 

Solution: 

The  product  of  the  base  times  the  altitude  =  16X11  =  176. 

I  of  the  product  1 76  =  88. 

Therefore:    The  area  of  the  triangle  is  88  square  inches. 

In  finding  the  product,  be  sure  that  both  base  and  altitude 
are  expressed  in  the  same  linear  units.  Only  the  final  area, 
then,  will  need  to  be  labeled. 

Find  the  area  of  the  following  triangles : 


Altitude      X       Base     = 

Area. 

2. 

10 

ft. 

15     ft. 

? 

3. 

8 

in. 

12     in. 

? 

4. 

20 

rd. 

35     rd. 

? 

6. 

11 

in. 

19     in. 

? 

6. 

3 

4 

ft. 

If  ft. 

? 

7. 

6f 

in. 

12     in. 

? 

8. 

1.65  ft. 

2.3  ft. 

? 

9. 

.3 

yd. 

.5  yd. 

? 

10. 

4 

ft. 

2ift. 

? 

11.  A  field  in  the  shape  of  a  right  triangle  has  a  base  ol 
20  rods  and  an  altitude  of  16  rods.  Find  its  area  in  square 
rods.    How  many  acres  in  this  triangular  field? 

12.  A  diamond  (also  called  a  rhombus)  may 
be  divided  into  2  equal  triangles.    If  the  short 
diagonal  is  6  inches  and  the  long  diagonal  8 
inches,  find  the  area  of  the  diamond. 
(Hint — The  two  diagonals  are  perpendicular  to  each  other  and  bisect 
each  other.) 


162 


SEVENTH  YEAR 


13.  If  the  barn,  of  which  the  end  is  shown 
in  the  illustration,  is  36  feet  long,  find  the 
total  number  of  square  feet  in  the  sides  and 
ends  of  the  barn? 

14.  How  much  would  it  cost  to  paint  the 
above  barn  at  10 j^  per  square  yard? 

15.  A  tract  of  ground  40  feet  square  is  divided  into  4  equal 
triangles  by  diagonal  lines.    What  is  the  area  of  each  triangle? 

16.  The  area  of  a  triangle  is  35  square  feet  and  the  altitude 
is  10  feet.     What  is  the  length  of  the  base  ? 

Solution:  Since  the  area  of  a  triangle  is  ^  of  the  product 
of  the  base  X  altitude,  the  product  of  the  base  times  the  altitude 
must  be  2X35  square  feet  =  70  square  feet.  If  the  product 
of  the  base  X  altitude  is  70  and  the  altitude  10,  the  base  must 
be70-M0or7. 

Therefore:    The  base  of  the  triangle  =  7  feet. 

Find  the  missing  term  in  the  following  problems: 

Altitude  of  triangle       Base  of  triangle     Area  of  triangle 


17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 


5  ft. 
? 

7  in. 

3 

4 


1ft. 


? 

5  yd. 
20  rd. 

7  ft. 

fft. 
16  in. 


? 

9  in. 

? 

? 

.32  rd. 

7^  yd. 

15  rd. 

? 

Uft. 


25  sq.  ft. 

54  sq.  in. 

28  sq.  in. 

I  sq.  ft. 

.384  sq.  rd. 

? 

? 

21  sq.  ft. 
? 

96  sq.  in. 


27.  Find   illustrations   of   triangles   in   your   neighborhood 
and  prepare  problems  for  the  class  to  solve. 


MEASUREMENTS— CONSTRUCTIONS 


163 


Constructions  used  in  Measurement 

When  a  carpenter  builds  a  house  he  follows  a  plan 
that  is  very  accurately  drawn  by  an  architect.  The 
architect  draws  this  plan  by  the  use  of  a  drawing 
board,  T-square,  rule,  triangles,  compass  or  dividers,  a 
curve  and  various  other  mechanical  drawing  instru- 
ments. The  following  constructions  are  performed 
with  only  two  of  these  instruments — the  compass 
and  the  rule.' 

If  you  study  geometry  you  will  learn  how  to  prove 
that  these  constructions  are  correct. 


Compass 


1.  Construct  a  perpendicular  at  a  given  point  in  a  line. 


># 


Place  the  sharp  point  of  the  compass  on  the  point 
P.  With  the  points  of  the  compass  spread  apart 
any  convenient  distance  as  from  A  to  P,  describe 
two  short  curved  Hnes  (called  arcs)  at  the  points 
A  and  B.     Spread  the  points  of  the  compass  farther        '  ^        '     '* 

apart  and  using  A  and  B  in  succession  as  centers 
describe  two  arcs  crossing  at  O.    The  line  drawn  from  O  to  P  is  perpen- 
dicular to  the  line  AB.     What  kind  of  angle  is  OPA. 


2.  Drop  a  perpendicular  from  a  point  to  a  line. 


Place  the  point  of  the  compass  at  P.  With  the 
points  of  the  compass  spread  farther  apart  than  the 
distance  from  P  to  the  given  hne,  draw  an  arc  cross- 
ing the  given  line  at  the  points  A  and  B.  Then  us- 
ing A  and  B  as  centers  and  the  compass  spread 
farther  apart  than  half  the  distance  from  A  to  B, 
draw  two  arcs  crossing  at  the  point  O.  The  line 
from  P  to  O  is  perpendicular  to  the  given  line  AB. 


1  If  drawing  boards,  T-squares,  and  triangles  are  available,  the  methods 
of  performing  these  same  constructions  in  a  much  easier  way  with  those 
mechanical  drawing  instruments  should  be  shown. 


164  SEVENTH  YEAR 


3.  Construct  an  angle  equal  to  a  given  angle. 


.^ 
•^ 


With  the  compass  spread  apart  at  any  convenient  dis- 
tance and  using  A  as  a  center,  draw  an  arc  cutting  the  two 
sides  of  the  angle  at  points  C  and  D.  Using  B  as  a  center 
and  the  compass  spread  as  before,  draw  an  arc  across  the 
given  line  BX  at  the  point  E.  Place  one  point  of  the  com- 
pass at  C  and  adjust  it  so  the  other  point  falls  at  D.  With 
E  as  a  center,  describe  an  arc  cutting  the  other  arc  at  F. 
Draw  the  line  BF.    The  angle,  FBE  is  the  required  angle. 


4.  Construct  a  line  parallel  to  a  given  line  through  a  given 
point. 

Draw  a  line  XY  through  the  point  P  and  cutting 
the  line  AB  at  any  convenient  angle  (as  Angle  1). 
At  the  point  P  construct  angle  2  equal  to  Angle  1. 
The  Une  MN,  drawn  through  points  P  and  O,  is 
parallel  to  the  line  AB. 

6.  Construct  an  equilateral  triangle,  with  a  given  side. 

Adjust  the  compass  so  that  one  point  rests  on  A  and  the 
other  point  on  B.  With  the  compass  spread  at  this  distance 
and  using  A  and  B  as  centers,  describe  two  arcs  crossing  at 
point  O.  Draw  the  sides  AO  and  BO.  The  triangle  ABO  is 
an  equilateral  triangle. 

6.  Construct  a  parallelogram  with  two  sides  and  the  angle 
between  those  sides  given. 


/ 


With  the  compass  spread  at  the  distance  AB  and 
using  C  as  a  center,  describe  an  arc  XY.  With  B  as 
a  center  and  the  compass  spread  to  the  distance  AC, 
draw  an  arc  MN  cutting  arc  XY  at  the  point  D. 
Draw  CD  and  BD.  The  figure  ABDC  is  the  re- 
quired parallelogram. 


7.  Construct  a  square. 

8.  Construct  an  isosceles  triangle. 


PAPER,  PRINTING  AND  BOOKBINDING       165 

APPLIED  REVIEW  PROBLEMS 
Print  Paper 


1 

1                         ' 

A  Modern  Paper  Mill 

Next  to  food,  clothing  and  shelter,  paper  is  probably  the 
most  important  necessity  in  modern  civilization.  Make  a  list 
of  the  various  ways  in  which  paper  is  used.  See  which  member 
of  the  class  can  make  the  largest  list. 

Print  paper,  used  in  our  daily  newspapers,  is  made  from  wood 
pulp.  The  spruce  tree  furnishes  the  best  wood  for  making 
print  paper.  These  trees  are  sawed  into  blocks  of  proper 
length  and  ground  by  stone  rollers,  on  which  water  is  dripping, 
into  a  very  fine  pulp.  Chemicals  are  mixed  with  some  of  the 
wood  in  order  to  toughen  the  fibers  so  that  the  paper  will  not 
tear  easily.  The  wood  pulp  is  collected  on  a  wire  form  and  run 
through  a  series  of  rollers,  being  dried  during  the  process. 

Exercise  1 

1.  It  takes  113.92  cubic  feet  of  timber  to  make  1  ton  of 
print  paper.    This  is  what  part  of  a  cord,  expressed  decimally? 

2.  A  spruce  tree  2  feet  in  diameter  will  produce  approxi- 
mately 1.8  tons  of  print  paper.  How  many  cubic  feet  of  wood 
are  there  in  such  a  tree? 

3.  How  many  cords  of  wood  are  there  in  a  tree  of  that  size? 
How  much  would  this  wood  be  worth  at  $3.50  per  cord? 


166 


SEVENTH  GRADE 


4.  Allowing  for  waste,  and  counting  8  J  board  feet  for  each 
cubic  foot,  what  would  be  the  value  of  the  lumber  in  such  a 
tree  at  $28.60  per  M? 

6.  Find  the  value  at  6§  cents  per  pound  of  the  print  paper 
that  may  be  manufactured  from  a  tree  of  that  size.  Compare 
the  values  of  the  paper,  lumber  and  wood  from  such  a  tree. 

Print  paper  is  shipped  from  a 
certain  paper  mill  in  rolls  having  an 
average  weight  of  1700  pounds.  The 
width  of  the  paper  in  these  rolls  is 
75  f  inches. 

6.  A  strip  of  this  paper  1  foot  in 
length    and    the    width    of    the    roll 
weighs  l^g^  ounces.    What  is  the  length  of  one  of  these  1700 
pound  rolls  in  feet? 

7.  How  many  miles  long  is  one  of  these  rolls? 

A  daily  paper,  on 

a  certain  day,  issued 
an  edition  of  100,000 
32-page  papers,  the 
size  of  each  page  being 
18i"  X  23i".  Each 
print  paper  roll 
weighed  1650  pounds. 
The    width    of    the 

A  Modern  Newspaper  Press  paper    WaS    73    inchcS 

and  its  average  weight  per  foot  in  length  was  1^  ounces. 

8.  What  was  the  length  of  a  roll  of  this  paper  in  feet? 

9.  What  was  the  length  of  a  roll  in  miles? 

10.  How  many  sheets  were  there  in  each  32-page  paper? 

11.  How  many  times  is  the  width  of  a  sheet  of  the  paper 
contained  in  the  width  of  the  roll? 


PAPER,  PRINTING  AND  BOOKBINDING       167 

12.  How  many  inches  in  length  would  be  used  to  print  one 
32-page  paper? 

13.  Each  roll  will  print  how  many  papers?    (See  Prob.  11.) 

14.  How  many  rolls  of  this  paper  were  required  for  the 
edition  of  100,000  papers?  How  many  tons  would  these  rolls 
weigh? 

15.  How  many  trees  of  the  size  stated  in  Problem  2  were 
required  to  produce  the  wood  pulp  used  in  manufacturing  the 
paper  for  this  edition? 

Type 

Look  at  this  page  and  see  how  many  kinds  of  type  and  other 
characters  are  used.  The  typ>e  in  this  line  is  designated  as 
"10  point."  The  type  in  the  lines  at  the  bottom  of  this  page 
is  known  as  "8  point."  The  type  in  the  line  at  top  of  the 
illustration  is  "6  point." 

Type  sizes  are  classified  by  "points" 
and  for  this  purpose  the  inch  is  divided 
into  72  parts  or  "points."  "12  point," 
which  is  a  standard  of  measurement 
(commonly  called  pica),  is  ^  of  an 
inch  high,  and  "6  point"  is  -^2  of 
an  inch  high. 

In  printing,  the  term  "em"  applies  to  the  exact  square 
space  occupied  by  a  single  letter  counted  as  wide  as  it  is  high.^ 
The  "em"  is  the  unit  of  measure  of  the  quantity  of  type  on  a 
page. 

The  number  of  lines  on  a  page  varies  with  the  size  of  the 
type  and  the  amount  of  space  separating  the  lines. 

*As  a  matter  of  fact,  the  type  letter  is  so  made  as  to  require  less  space 
sideways  than  up  and  down.  On  this  account,  letters  and  figures  are 
measured  by  their  depth  and  not  their  width. 


Comparison  of  Type 

D 

6  Point 

n 

8  Point 

D 

10  Point 

D 

12  Point 

168  SEVENTH  YEAR 

Exercise  2 

1.  "6  point"  type  is  what  part  of  an  inch  high? 

2.  "8  point"  type  is  what  part  of  an  inch  high? 

3.  "10  point"  type  is  what  part  of  an  inch  high? 

4.  "12  point"  type  is  what  part  of  an  inch  high? 

5.  Measure  very  accurately  one  of  the  lines  on  this  page. 
How  many  picas  wide  is  it? 

6.  Counting  70  letters  to  an  8  point  line  and  38  lines  to  a 
page,  how  many  "ems"  would  a  page  contain?  (An  "em" 
is  equivalent  to  an  average  of  two  characters — letters,  figures, 
or  punctuation  marks.) 

7.  Counting  58  letters  to  a  line  and  33  lines  to  a  page,  how 
many  "ems"  would  a  "10  point"  page  contain? 

8.  Counting  48  letters  to  a  line  and  28  lines  to  a  page,  how 
many  "ems"  would  a  "12  point"  page  contain? 

Book  Making 

The  paper  used  for  school  books  is  necessarily  of  a  much 
better  quality  than  the  print  paper  used  by  newspapers. 
With  wood  pulp  must  be  combined  a  certain  percentage  of 
"rags"  (cotton  or  linen)  to  make  this  higher  grade  of  paper. 

Instead  of  this  kind  of  paper  being  shipped  in  rolls  it  is 
marketed  flat  and  sold  by  the  ream,  500  sheets  to  the  ream. 

By  a  close  inspection  of  the  top  of  this  book,  it  will  be  seen 
that  it  is  bound  in  sections  of  32  pages  (16  leaves)  each,  called 
forms. 

Exercise  3 

1.  Divide  the  total  number  of  pages  in  this  book,  including 
the  6  introductory  pages  in  the  front  of  the  book,  by  32  and  see 
how  many  "forms"  are  required. 


PAPER,  PRINTING  AND  BOOKBINDING       169 

2.  Take  a  sheet  of  paper  31"  by  21"  and  fold  it  successively 
4  times.  Open  it  up  sufficiently  to  enable  you  to  number  the 
pages  in  regular  order  (as  they  would  open  if  the  edges  were 
cut)  from  1  to  32.  Then  spread  the  sheet  out  flat  and  see  how 
the  plates  are  arranged  in  printing  a  form. 

3.  Counting  both  sides  of  the  sheet,  how  many  printing 
impressions  are  required  in  printing  one  book  of  this  size? 

4.  How  many  sheets  of  the  size  stated  are  used  in  making 
one  book? 

5.  How  many  books  will  1  ream  of  paper  make? 

6.  How  many  reams  of  paper  are  needed  for  an  edition  of 
25,000  copies  of  this  book? 

7.  Assuming  that  each  ream  of  this  paper  weighs  75  pounds, 
what  weight  of  paper  is  required  for  an  edition  of  25,000  books? 

Book  Binding 

A  very  important  step  in  book  making  is  the  binding.  This 
may  be  of  paper,  of  cloth,  of  leather,  or  of  some  combination  of 
these  materials.    School  books  are  usually  full  cloth  bound. 

The  printed  forms,  which  are  folded  by  machinery  as  they 
come  from  the  press,  are  ordinarily  of  32  pages,  although  in 
larger  books  they  may  be  of  64  pages. 

Exercise  4 

1.  If  the  glueing  and  re-enforcing  of  the  "back  bone" 
of  each  book,  before  the  cover  is  put  on,  requires  an  average  of 
^  minute  per  book,  how  many  working  days  of  8  hours  would  it 
require  for  one  person  to  care  for  that  part  of  an  edition  of 
25,000  books? 

2.  The  cloth  required  for  the  outside  of  this  book  is  cut 
approximately  8^"  by  12".  How  many  yards  of  binding  cloth 
36  inches  wide  are  needed  for  25,000  copies? 


170 


SEVENTH  YEAR 


3.  If  the  "binders'  board"  which  is  used  inside  of  the  cloth 
cover  is  cut  7^"x5  j",  how  many  sheets  of  board,  size  22"x28" 
would  be  required  for  an  edition  of  25,000  books? 


Exercise  5 

The  announced  circulation  of  a  metropolitan  daily  newspaper 
for  a  certain  date  was  681,562  papers  of  80  pages  each.  The 
following  facts  were  included  in  this  newspaper's  statement 
explaining  the  issue.  This  illustrates  the  extensive  use  of 
timber  in  the  production  of  print  paper  alone. 


It  required  the  usable  timber  from 
84  acres  to  produce  the  amount  of 
paper   needed  for   this   one   issue. 

It  required  425  tons  of  paper  for  this 
one  issue. 

It  required  the  labor  of  510  men  4 
days  to  malte  the  output  of  paper  for 
this  one  issue. 

It  required  a  train  of  15  cars,  each 
carrying  28  tons,  to  transport  this 
paper  from  the  mills  to   the  city. 

It  required  60  truclcloads,  each 
weighing-  7  tons,  to  deliver  this  paper 
from  the  railroad. 

It  would  make  a  paper  path  18 
inches  wide  and  10,843  miles  in  length 
if  the  sheets  required  for  this  one  issue 
were  spread  out  end  to  end.  This 
would  be  sufficient  to  stretch  from 
Bering   Strait   to   Cape   Horn. 

It  would  paper  an  expanse  of  85,- 
876,560  square  feet  if  spread  out  in 
single  sheets  over  a  flat  surface. 


1.  80  pages  means  how 
many  single  sheets,  or 
leaves? 

2.  The  size  of  the  news- 
paper here  referred  to  is 
18  J  inches  by  23^  inches. 
What  is  the  length,  in 
inches,  of  one  paper  of  this 
issue,  the  sheets  laid  end 
to  end?  The  length  in 
feet? 

3.  Multiply  this  num- 
ber of  feet  by  681,562 
papers,  and  reduce  to 
miles. 


4.  How  many  square  inches  in  one  single  sheet  of  this 
paper?    In  the  40  sheets  (80  pages)  of  this  paper? 

6.  How  many  square  feet  are  there  in  one  full  paper  of 
this  issue?     An  acre  contains  how  many  square  feet? 

6.  Reduce  85,876,560  square  feet  to  acres.     How  many 
160-acre  farms  would  this  amount  of  paper  cover? 


PART  II 
Training  for  Efficiency.    Checking  Up 


It  is  considered  good  business  practice  to  check  all  bills  and 
accounts  to  be  sure  that  they  are  accurate.  In  order  to  do  this 
checking  rapidly  and  accurately,  practice  on  the  different  com- 
putations that  are  used. 

Since  no  business  man  wishes  his  work  delayed  by  slow 
checking,  it  is  important  that  short  methods  be  used  whenever 
it  is  possible.  The  following  pages  not  only  give  examples 
for  rapid  work,  but  also  show  some  of  the  short  methods  that 
are  commonly  used. 

In  striving  for  efficiency  in  rapid  computations,  use  a  pencil 
just  as  little  as  possible.  Pencil  and  paper  are  not  always  at 
hand  and  it  is  therefore  necessary  to  make  mental  computations 
to  check  the  work.  It  is  often  sufficient  to  estimate  a  result 
roughly  and  then  check  more  accurately  at  one's  leisure. 
Practice  in  this  type  of  checking  can  be  secured  by  estimating 
results  approximately  in  order  to  check  solutions  of  problems. 


171 


172  EIGHTH  YEAR 

CHAPTER  I 
Exercise  1 

Practice  on  the  first  ten  examples  in  this  exercise  imtU  you 
can  do  all  of  them  correctly  in  5  minutes. 

1.                       2.                       3.  4.  6. 

2496                 8765                 2340  5426  1982 

1983                 4312                 5864  3798  4651 

7218                 9736                 3217  4125  3928 

4520                 1326                 8629  7864  5416 

6924                 5298                 4837  3907  7718 

6.                       7.                          8.  9.  10. 

3178                 3927                 7856  4455  3792 

4056                 8220                 9742  6872  4891 

2792                 4065                 6319  9987  7726 

3695                 3918                 2390  2436  3555 

9781                 4639                 2945  2856  4930 


Double-Column  Addition 

11.  In  adding  sales  slips  where  there  are  usually  only  two 

j^  columns,  clerks  sometimes  add  two  columns  at  a  time.       Be- 

rt- ginning  at  the   bottom   of  example  11,  to  the  18  add  the 

5  tens  or  50.     18  +  50  =  68.     To  the  68  add  the  3  units 
(of  the  53)  =  71.     71  +  20  =  91.      91  +  5  =  96.      96  + 


53 


18  10  =  106.      106  +  4  =  110. 

Use  double-column  addition  for  the  following  problems : 
12.  18.  14.  16.  16.  17.  18.  19. 


18 

24 

37 

12 

30 

16 

35 

13 

32 

19 

22 

40 

26 

28 

28 

40 

20 

45 

14 

34 

42 

30 

20 

25 

16 

30 

26 

19 

15 

15 

50 

18 

45 

15 

18 

16 

25 

38 

17 

14 

REVIEW  EXERCISES 


173 


Exercise  2 

We  should  be  able  to  add  horizontally  (or  across  a  page) 
as  well  as  vertically  (up  or  down).  By  adding  both  ways  you 
get  a  "cross  check"  on  the  correctness  of  your  additions. 
Work  on  the  following  problems  until  your  results  "crosscheck." 


1. 

87+43+26+29=   |S6 
16    23    58    94=  :>o  | 
63    05    41     89  = 
27    96    38    42  = 
81     27    96    54  = 


> 


57+36+29+14: 
76  12  45  38: 
67  84  15  29: 
47  36  91  28: 
56  18  72  39: 


43+65+81+71: 
21  58  64  37: 
83  41  92  65: 
61  23  59  84: 
95  64  32  81: 


32+56+98+41: 
72  65  41  89  = 
68  24  15  97  = 
41  36  89  27  = 
19  72  43  86  = 


6. 

61+57+84+93  = 
68  54  71  29: 
80  95  43  16  = 
29  85  47  13  = 
37  68  95  82  = 


6. 

14+50+97+83: 
26  81  43  93: 
80  36  12  75: 
41  67  83  25  = 
59  88  64  97  = 


73+96+81+24  = 
63  75  98  26: 
25  76  31  48  = 
58  19  86  57  = 
76  84  39  46  = 


8. 

25+83+17+94  = 
52  78  61  27  = 
76  19  94  53  = 
15  64  82  23  = 
82  93  47  90  = 


174  EIGHTH  YEAR 

Exercise  3 

Subtract  the  first  10  examples  as  a  speed  test.    Keep  a  record 
of  your  time.    You  should  be  able  to  do  them  in  2  minutes. 

1.  2.  3.  4.  5. 

2,164  3,986  4,000  2,859  10,100 

1,907  2,497  3,179  1,964  2,786 


6. 

7. 

8. 

9. 

10. 

10,724 

29,847 

32,809 

40,400 

21,610 

9,847 

18,858 

14,987 

3,976 

19,143 

11.  The  area  of  Texas  is  265,896  square  miles.  How  much 
larger  in  area  is  Texas  than  Rhode  Island,  which  has  an  area 
of  1248  square  miles? 

12.  The  population  of  the  United  States  in  1910,  exclusive 
of  the  detached  possessions,  was  92,228,531.  Including  the 
detached  possessions,  it  was  101,102,677.  What  was  the 
population  of  the  detached  possessions? 

13.  If,  as  computed,  the  water  area  of  the  earth  is  approxi- 
mately 144,500,000  square  miles,  and  the  total  surface  of  the 
earth  is  approximately  196,907,000  square  miles,  how  much 
more  water  surface  than  land  is  there? 

14.  The  ancients  believed  one-seventh  of  the  earth's  surface 
to  be  water.  This  would  be  approximately  20,642,857  square 
miles.    How  great  was  their  error  as  to  the  amount? 

15.  The  distance  from  New  York  to  San  Francisco  by  sea, 
by  way  of  Cape  Horn,  is  reckoned  at  13,000  miles.  By  way  of 
the  Panama  Canal  it  is  reckoned  at  5278  miles.  How  much 
shorter  is  the  Panama  route? 

16.  A  bushel  contains  2150.42  cubic  inches  and  a  cubic  foot 
1728  cubic  inches.  How  much  does  the  bushel  exceed  the 
cubic  foot  in  size? 


REVIEW  EXERCISES— SPEED  TESTS  17b 

Exercise  4 

Since  the  subtrahend  and  the  difference  together  equal  the 
minuend,  in  subtraction,  any  one  of  the  three  can  be  easily 
supplied  if  the  others  are  given.    Supply  the  subtrahends : 


1.  2,837 

2.  20,000 

3.  240,000 

1,956 

18,276 

20,700 

4.  3,500 

5.  401,286 

6  546,280 

3,080 

297,497 

397,149 

7.  5,962 

8.  954,362 

9.  717,400 

3,000 

100,000 

200,099 

10.  75,160 

11.  400,000 

12.  100,000 

42,839 

286,934 

66,752 

13.  19,763 

14.  79,080 

16.  327,861 

11,274  16,111  100,000 

SPEED  TESTS  IN  MULTIPLICATION 
Exercise  6.    Time:  3  minutes 
Multiply: 


9389 

2459 

6382 

6195 

2574 

5 

2 

7 

3 

8 

3429 

9837 

5289 

4562 

3768 

9 

4 

6 

5 

2 

5497 

3869 

8576 

6542 

6347 

7 

8 

9 

4 

6 

'6 

EIGHTH  YEAR 

Exercise  6. 

Time: 

5  minutes 

Multiply: 

2459 

6382 

9837 

3429 

82 

75 

46 

39 

3768 

5497 

6542 

8576 

28 

57 

64 

93 

SHORT  METHODS  EN  MULTIPLICATION 
1.  345X10  =  3450 
3.45X10  =  34.5 
To  multiply  an  integer  by  10,  add  a  zero  to  the  number. 
To  multiply  a  decimal  by  10,  move  the  decimal  point  one 
place  to  the  right. 
Read  the  products  without  using  a  pencil : 

2.  68  X10=  6.     120X10=  10.    45.6X10  = 

3.  231X10=  7.  5.03X10=  11.    9.74X10  = 

4.  4.63X10=  8.  23.4X10=  12.    860  X10  = 

5.  938X10=  9.     .48X10=  13.  10.35X10  = 
14.  John  has  $2.75  and  his  brother  has  10  times  as  much  in 

the  bank.    How  much  has  his  brother  in  the  bank? 

16.  The  lumber  in  a  book  rack  costs  15  cents.  The  lumber  in 
a  medicine  chest  costs  10  times  as  much.  Find  the  cost  of  the 
lumber  in  the  medicine  chest. 

Exercise  7 

1.    42  X 100 =4200. 
.427X100=42.7 
To  multiply  an  integer  by  100,  add  two  zeros  to  the  number. 
To  multiply  a  decimal  by  100,  move  the  decimal  point  two 
places  to  the  right. 


REVIEW  EXERCISES  177 

Give  products  without  using  a  pencil : 

2.  .625     X100=         7.  .7854X100=  12.  83      X100  = 

3.  68        X100=         8.  471    X100=  13.  62.5  X100  = 

4.  .5236  X100=         9.  32.5  XlOO=  14.  45      XlOO  = 

5.  527      X100=       10.  628    X100=  15.  .0625X100  = 

6.  3.1416X100=       11.  52.3  XlOO=  16.  42.85X100  = 

17.  Show  a  short  method  of  multiplying  a  number  by  200; 
by  300;  by  400;  by  500. 

18.  Show  a  short  method  of  multiplying  a  number  by  1000; 
by  2000;  by  3000;  by  4000. 

19.  A  school  bought  100  pamphlets  on  soil  fertility  at  $.06 
each.    How  much  did  the  100  cost? 

20.  A  man  bought  a  farm  of  157  acres  at  $100  per  acre. 
How  much  did  the  farm  cost? 

Exercise  8 

1.  344X  25  =  34,400  =8600. 

4 

2.  344  X 125  =  344,000  =  43,000. 

8 

To  multiply  a  number  by  25,  multiply  the  number  by  100 
and  divide  by  4. 

To  multiply  a  number  by  125,  multiply  the  number  by  1000 
and  divide  by  8. 


Vi 

thout  pencil : 

3. 

44X  25  = 

7. 

15X  25    = 

11. 

64X125  = 

4. 

24X125  = 

8. 

12X$  .25  = 

12. 

128  X  25  = 

6. 

32X  25  = 

9. 

18X$1.25  = 

13. 

32X125  = 

6. 

72X125  = 

10. 

244X  25    = 

14. 

88X  25  = 

178  EIGHTH  YEAR 

16.  My  father  bought  a  farm  of  80  acres  at  $125  per  acre. 
How  much  did  the  farm  cost  him? 

16.  A  farmer  sold  a  herd  of  12  calves  at  $25  each.    How  much 
did  he  receive  for  the  herd? 

17.  Give  a  short  method  of  multiplying  a  number  by  50. 

18.  Give  a  short  method  of  multiplying  a  number  by  75. 

FRACTIONAL  PARTS  USED  IN  SHORT  METHODS 

Exercise  9 

33 J  =  J  of  100.  12j  =  J  of  100. 

16f  =  iofl00.  66|  =  Jof200. 

1.  Show  that  multiplying  a  number  by  100  and  dividing  by 
3  is  the  same  as  multiplying  the  number  by  33|^. 

2.  Show  a  short  method  of  multiplying  a  number  by  16f . 

3.  State  a  short  method  of  multiplying  a  number  by  12^. 

4.  State  a  short  method  of  multiplying  a  number  by  66f . 
Without  pencil  give  the  following  products : 

6.    45X33  J  13.  16X12|  = 

6.  36Xl6f  14.  72X33j  = 

7.  128  X 12 J  =  15.  63X66|  = 

8.  6X66f  =  16.  42Xl6f  = 

9.  32Xl2j=  17.  40Xl2j  = 

10.  216X33j=  18.  12X66f  = 

11.  252X66|=  19.  84X16f  = 

12.  246Xl6f  =  20.  96Xl2j  = 

21.  A  merchant  bought  a  bolt  of  dress  goods  containing  40 
yards  at  33|  cents  a  yard.    How  much  did  the  bolt  cost? 

22.  A  banker  bought  a  tract  of  timber  containing  33  J  acres 
at  $60  per  acre.     How  much  did  he  pay  for  the  tract? 


REVIEW  EXERCISES  179 

Exercise  10 

1.  Multiply  45  by  99. 

100X45=4500 

Subtracting:       1X45=     45 

99X45  =  4455 

To  multiply  a  number  by  99,  multiply  the  number  by  100 
and  subtract  the  number  from  that  product. 

2.  84X99=  4.  246X99=  6.  420X99  = 

3.  37X99=  5.  854X99=  7.  575X99  = 

8.  By  comparison  with  the  above  method  show  how  to 
multiply  a  number  by  9. 

9.  State  a  short  method  for  multiplying  a  number  by  999. 

10.  Show  how  to  multiply  a  number  by  49  by  a  short  method. 

11.  A  f -barrel  sack  of  flour  contains  49  pounds.    How  many 
pounds  are  there  in  44  such  sacks? 

12.  Show  short  methods  of  multiplying  by  19,  29,  39,  69,  etc. 

Exercise  11 

1.  Multiply  5  J  by  5  J. 

^2  In  multiplying  these  two  mixed  numbers, 

fig  we  have  the  products  5X5;  5X^;  2  X5;  and 

25  ^X|.     But  (5X^)  and  (iX5)  is  the  same 

2|  as  1X5.     We  then  have  (5X5)  +  (1X5)  or 

2^  6X5.    To  this  quotient  we  add  the  product 

_£  offxiori 

30j  5|X5|  =  (6X5)  +  (|x|)=30i. 

2.  Multiply  8 J X8i.    The  product=(9X8)  +  (Jxi)=72j. 

3.  4ix4i  =  ?  6.    7ix  7j  =  ? 

4.  6jx6i  =  ?  6.  12ixi2i  =  ? 


180 


EIGHTH  YEAR 


7.  What  is  the  cost  of  8^  pounds  of  nails  at  8f  cents  per  lb.? 

8.  What  is  the  cost  of  7f  pounds  of  apples  at  7§  cents 
per  pound? 

9.  Showthat8ix8f  =  (9X8)  +  (Jxf). 
10.  Show  that  9ix9f  =  (10X9)  +  (ixi). 


SPEED  TESTS  IN  DIVISION 

Exercise  12.  Time:  3  minutes 

5)1890 

9)6273                4)1584 

6)5244 

3)2919 

8)4768                2)1810 

7)6475 

9)4365 

6)5778                7)6118 
Exercise  13.    Time:  6  minutes 

8)3880 

92)29440 

39)15093 

61)53192 

55)45155 

83)58764 
Exercise  14.    Time:  8  minutes 

47)17578 

82)29602 

67)17152 

231)106953 

t7)227979 

945)574560 

927)377289 

SHORT  METHODS  IN  DIVISION 
Exercise  15 
To  divide  a  number  by  10,  100,  or  1000,  move  the  decimal 
point  to  the  left  one,  two,  or  three  places,  respectively,  prefixing 
zeros  if  necessary. 

1.  32-M0  =  3.2  2.  32  ^100  =  .32  3.  32 -J- 1000  =  .032 


REVIEW  EXERCISES  181 


4.67  -f-  10=    7.42.5  -4-1000=    10.  3475^1000  = 


6.  3.9^100=    8.  4.5 


100=    11.   675^1000  = 


6.  62.5-^  10=    9.  2.37 -r-  10=    12.  43.54-  100  = 

13.  I  bought  2450  board  feet  of  lumber  at  $80  per  thousand. 
How  much  did  I  pay  for  the  lumber? 

14.  A  man  shipped  50  sacks  of  potatoes  weighing  4995 
pounds.    How  many  hundredweight  did  he  ship? 

15.  How  much  was  his  freight  at  20  cents  per  cwt.? 

Exercise  16 

1.  Divide  4225  by  25. 

4X4225  =  16,900. 
16,9004-100=169. 
To  divide  a  number  by  25,  multiply  the  number  by  4  and 
divide  the  product  by  100. 

2.  15704-25=  6.  12254-25=  8.  4754-25  = 

3.  3454-25=  6.  18504-25=  9.  8754-25  = 

4.  6254-25=  7.  23154-25=  10.    724-25  = 

11.  A  merchant  bought  some  wash  ties  at  25  cents  each. 
How  many  would  he  get  for  $26.75? 

12.  Show  a  short  method  similar  to  the  above  for  dividing 
a  number  by  125. 

13.  A  farmer  paid  $20,000  for  a  farm.    If  he  paid  $125  per 
acre,  how  many  acres  did  he  buy? 

14.  A  real  estate  dealer  sold  a  tract  of  25  acres  of  rough 
pasture  land  for  $1125.     What  was  the  selling  price  per  acre? 

16.  My  neighbor  bought  a  tract  of  unimproved  land  for 

$6175  at  $25  per  acre.    How  many  acres  did  he  buy? 

Pupils  should  be  encouraged  to  use  these  short  methods  in  every  prob- 
lem where  they  apply. 


182  EIGHTH  YEAR 

Exercise  17 

To  divide  a  number  by  33|,  multiply  the  number  by  3  and 
divide  by  100.  Show  that  this  method  is  correct  by  using 
fractions. 

1.  Divide  400  by  33j. 

3X400  =  1200.     1200 -MOO  =  12. 
400  H- 33^  =  12. 

2.  750 -H  33 J  =  5.     75-^33j  = 

3.  900 -^  33 J  =  6.  125  ^33^  = 

4.  660  ^33 J  =  7.  480 -^33 J  = 

8.  Show  a  short  method  of  dividing  a  number  by  12  J. 

9.  Show  a  short  method  of  dividing  a  number  by  16|. 

10.  Show  a  short  method  of  dividing  a  number  by  66|. 

Exercise  18 

One  may  often  save  time  by  dividing  a  number  by  two 
factors  of  the  divisor. 

1.  Divide  774  by  18. 

3)774 

6)2^  774 -^  18 =43. 

43 

Perform  the  following  divisions  by  using  factors  of  the  divisor: 

2.  555-i-15=  5.  2720^32=  8.  1176-^56  = 

3.  1674 -^  27=  6.  2835-^45=  9.  2765 -^  35  = 

4.  688^16=  7.  2706-^33=  10.  1148-^28  = 

11.  A  farmer  raised  2860  bushels  of  corn  on  44  acres  of 
ground.    Find  the  yield  per  acre. 

12.  A  load  of  shelled  corn  weighed  1596  pounds.  A  bushel  of 
shelled  corn  weighs  56  pounds.  How  many  bushels  were  there 
in  the  load? 


REVIEW  EXERCISES  183 

REVIEW  OF  FRACTIONS 

The  different  processes  in  fractions  should  become  just 
as  familiar  to  us  as  the  four  fundamental  operations  in  whole 
numbers.  Practice  on  the  following  exercises  until  you  can 
do  each  of  them  in  2  minutes. 


_7L 4_    2 
12^^    3 


3  2 

4  ~    3 


3 

4 

+ 

4 
5 

= 

i 

+ 

a 

= 

a 



3 

4 

__ 

2 
3 

- 

f 

= 

8 

/N 

5 

~" 

8 

X 

3 

4 

= 

* 

X 

1 

4 

= 

i 

_i_. 

1^ 

-- 

3 

8 

-J- 

1 
2 

= 

3 
4 

+ 

2 
3 

__ 

Exercise  19 

7 
8 

+  4  = 

7 
12 

+  1  = 

Exercise  20 

7 

3 

8 

5    "~ 

8 

3 

9 

4    — 

Exercise  21 

f 

xi  = 

5 

x|  = 

6 

3 

8 

x4  = 

Exercise  22 

5 

.     3    _ 

8 

~    4   — 

5 
6 

-1  = 

Exercise  23 

4 

.     2    _ 

5 

^    3    - 

2 

1    _ 

3 

~    4    — 

i   \/   A   — 
5   '^    7    ~ 

15^^    5    — 

9    V    7    _ 
14  A  12  — 


2  _L.  7 

3  ~  ¥ 

3  .  2 

5  ~  7 


+  1  = 


7w4_  2_1_  7    ^    5 

8    ''^   ^  ~  3  4    ~  TT 


8 


Refer  to  pages  30  to  36  in  Part  I  for  explanations  of  these 
processes  if  they  are  not  clear. 


184  EIGHTH  YEAR 

MEKED  NUMBERS 
Exercise  24 
Add  the  following: 

1.  23f ,  45|,  82f ,  35f .  7.  From  23j  subtract  18j. 

2.  9i  13i,  16j,  8|,  11|.  8.  From    9j  subtract    Tf 

3.  7f ,  4j,  9f ,  12f ,  3 J.  9.  From  32|  subtract  19 J. 

4.  17 i,  25f ,  43i  32f ,  STf.  10.  From  20|  subtract  14f . 
6.  6j,  8|,  5i,  9f,  7i.  11.  From  5j  subtract  3f. 
6.  6|,  2f,  6|,  4|,  Ij.  12.  From  60  J  subtract  lOf. 

Exercise  25 

Find  the  following  products  and  quotients: 

1.  3|xlf  4.12    Xlf.  T.Divide    8f  by  2|. 

2.  8|x3f.  5.    3jx2f  S.Divide    3|by2. 

3.  lOiXlf.  6.  22JX2|.  9.  Divide  12 f  by  2|-. 

10.  In  a  track  meet  the  winner  of  the  running  broad  jump 
leaped  16 1-  feet.  His  nearest  competitor  jumped  15|^  feet. 
How  much  farther  was  the  first  jump  than  the  second? 

11.  A  square  rod  is  16^  feet  by  16|  feet.  How  many 
square  feet  are  there  in  a  square  rod? 

12.  Find  the  cost  of  7^  yards  of  gingham  at  37^  cents  a 
yard. 

13.  In  the  spring  of  1917  a  24^-pound  sack  of  flour  sold 
for  5^  cents  a  pound.    What  was  the  price  per  sack? 

14.  How  many  guest  towels  f  of  a  yard  long  can  be  made 
from  a  strip  of  linen  toweling  4^  yards  long? 

16.  Find  the  cost  of  if  pounds  of  steak  at  28  cents  a 
pound. 


REVIEW  OF  DECIMALS  185 

MISCELLANEOUS  PROBLEMS 
Exercise  26 
DECIMALS 

1.  Add:    8.25;  .072;  7.055;  .0075;  13.5;  .068. 

2.  Add:    .0054;  3.125;  11.2347;  3.1416;  .7854;  .866. 

3.  2150.42-1728  =  ?  6.  425.68-98.375  =  ? 

4.  6.5-1.4142  =  ?  6.  $2-$1.37  =  ? 

7.  Multiply  324.5  by  .035. 

8.  What  is  the  principle  of  pointing  off  decimal  places  in 
the  product? 

9.  .032X2.8  =  ?  12.  4.05 X. 62  =  ? 

10.  3.1416X25  =  ?  13.  63.3X25.7  =  ? 

11.  .0025X.03  =  ?  14.  .008 X. 0016  =  ? 
16.  Divide  8.575  by  3.43. 

16.  What  is  the  principle  for  pointing  off  decimal  places  in 
the  quotient? 

17.  .287^3.5  =  ?  20.  32.5-^260  =  ? 

18.  .02145^.007  =  ?  21.  82.25-^-25  =  ? 

19.  25.5-^425  =  ?  22.  .0025  4- .05  =  ? 

23.  Find  the  cost  of  7725  bricks  at  $16.25  per  thousand.^ 

24.  What  are  the  freight  charges  on  a  barrel  of  apples 
weighing  160  pounds,  at  $0.22  per  hundred  pounds? 

26.  A  chicken  weighing  4.25  pounds  cost  $1.02.     Find  the 
cost  per  pound. 

26.  Find  the  cost  of  225  feet  of  lumber  at  $67.50  per  1000 
feet. 

'Use  the  short  method  of  dividing  by  1000  to  find  the  number  of  thoii- 
nanda  of  brick. 


186  EIGHTH  YEAR 

Practice  Exercises  in  Decimals 

Hektograph  or  mimeograph  the  following  exercises  for  written 
speed  exercises.  Leave  room  for  the  work  to  be  done  on  the 
same  paper  with  the  exercises.  Use  the  following  time  limits 
for  written  work : 

Excellent — 1  mirute;  Good — 1^  minutes;  Fair — 2  minutes. 

Exercise  A 

Copy  in  column  form  and  add : 

1.  .05;  2.005;  .875;  25.2. 

2.  31.416;  .0005;  1.025;  3.52. 

3.  .075;  .0515;  .03;  5.042. 

Exercise  B 
Copy  in  column  form  and  subtract: 

1.  8.05  -  6.173.  4.  8  -  3.125. 

2.  1.435  -  .8725.  6.  25.05  -  16.3. 

3.  5.5  -  2.375.  6.  7.025  -  2.55. 

Exercise  C 
Copy  in  column  form  and  add : 

1.  12.375;  .05;  1.025;  3.1416. 

2.  1.075;  5.2;  12.5;  62.5. 

8.  25.25;  .0125;  .005;  2.055. 

Exercise  D 
Copy  in  column  form  and  subtract: 

1.  9.4  -  3.75.  4.  2.375  -  1.075. 

2.  .895  -  .0325.  6.  1.928  -  .742. 

3.  15  -  6.625.  6.  5.5  -  2.343. 


PRACTICE  EXERCISES  IN  DECIMALS 


187 


Exercise  E 

Place  the  decimal  point  in  its  proper  position  in  each  of  the 
following  products: 

1—25 
42.25  24.5  6.25  .135  425 

.3  3.2  2.8  .09  .45 


12375 

7840 

17500 

1215 

19125 

48.35 

847.2 

8.75 

•.875 

1.414 

.05 

.4 

25 

4.6 

8.5 

24175 

33888 

21875 

40250 

120190 

4.078 

49.52 

482.5 

.0567 

4.52 

.09 

.6 

1.2 

.38 

9.06 

36702 

29712 

57900 

21546 

409512 

6.358 

9.175 

.0568 

50.25 

.5326 

2.8 

4.06 

4.06 

1.24 

36 

178024 

3725050 

230608 

623100 

191736 

62.25 

5.375 

4.325 

9.873 

69.45 

2.04 

.038 

204 

1.8 

8.2 

1269900 


204250 


882300 


177714 


569490 


Exercise  F 

The  figures  for  the  quotients  in  these  division  problems  are 
given  in  parentheses  at  the  side  of  the  dividends.  Place  the 
quotients  in  their  proper  places  above  the  dividends  and  point 
them  off. 


1.     .5)6.25  (125)         3.  .09)2.718  (302)       5.      7)29.47  (421) 


2.  3.1)25.079  (809)     4.  .25)46.75  (187)       6.  .15)9.525  (635) 


7.  5.01)3.7074  (74) 


8.  2.54)193.04 


188  EIGHTH  YEAR 

REVIEW  OF  PERCENTAGE 
Exercise  27 

1.  80%  of  520  eggs  placed  in  an  incubator  hatched.  How 
many  of  the  eggs  hatched?    How  many  did  not  hatch? 

2.  The  leaves  of  an  alfalfa  plant  constitute  45%  of  its 
weight.  How  many  pounds  of  leaves  are  there  in  a  ton  of 
alfalfa  hay?    How  many  pounds  of  stems  in  a  ton? 

3.  A  girl's  spelling  paper  was  marked  96%  correct.  How 
many  words  did  she  spell  correctly  out  of  50? 

4.  A  hog  shrinks  about  33|%  on  being  dressed.  What  is 
the  dressed  weight  of  a  210-pound  hog? 

6.  Which  would  you  rather  have— 20%  of  $864  or  25%  of 
$725? 

6.  There  are  525,000,000  acres  of  improved  land  in  the 
United  States.  About  20%  of  that  amount  is  planted  each 
year  in  corn.   Find  the  number  of  acres  devoted  to  raising  corn. 

7.  A  farmer  took  four  100-pound  cans  of  milk  to  the  cream- 
ery. The  milk  tested  3.8%  of  butter  fat.  How  many  pounds  of 
butter  fat  were  there  in  the  four  cans? 

8.  85%  of  butter  is  butter  fat.  How  many  pounds  of  butter 
fat  are  there  in  a  5-pound  jar  of  butter? 

9.  Ice  is  91.7%  as  heavy  as  water.  A  cubic  foot  of  water 
weighs  62 §  pounds.    How  much  does  a  cubic  foot  of  ice  weigh? 

10.  Sandstone  is  235%  as  heavy  as  water.  Find  the  weight 
of  a  cubic  foot  of  sandstone. 

11.  A  manufacturer  makes  a  stove  at  a  cost  of  $18.00. 
He  sells  it  to  a  retail  customer  at  a  gain  of  20%.  The  retail 
dealer  pays  $1.60  freight  and  sells  it  to  a  farmer  at  a  profit  of 
25%.    Find  the  price  paid  by  the  farmer. 


REVIEW  OF  PERCENTAGE  189 

Exercise  28 

1.  A  pint  is  what  per  cent  of  a  quart? 

2.  A  foot  is  what  per  cent  of  a  yard? 

3.  A  peck  is  what  per  cent  of  a  bushel? 

4.  A  farmer  planted  45  acres  of  corn  on  a  farm  of  160  acres. 
What  per  cent  of  his  farm  is  in  corn? 

5.  A  certain  prize  cow  yielded  21,944  pounds  of  milk  in  a 
year.  Her  milk  contained  944  pounds  of  butter  fat.  What 
per  cent  of  butter  fat  did  her  milk  contain? 

6.  A  farmer  tested  .180  kernels  from  one  lot  of  seed  corn, 
and  14  kernels  failed  to  grow.      What  per  cent  failed  to  grow? 

7.  The  same  farmer  tested  160  kernels  from  another  lot  of 
seed  corn  and  found  26  kernels  that  failed  to  sprout.  What 
per  cent  of  this  lot  failed  to  grow?  Which  lot  would  be  best 
for  planting? 

8.  There  are  135  boys  in  a  school  of  250  pupils.  What  per 
cent  of  the  pupils  are  boys?    What  per  cent  are  girls? 

9.  Fred  played  in  10  ball  games  during  the  summer.  He 
was  at  the  bat  50  times  and  made  16  base  hits.  What  was  his 
per  cent  of  base  hits?  Compare  his  percentage  of  base  hits 
with  your  favorite  player  in  the  big  leagues. 

10.  A  grammar  school  basket  ball  team  won  9  out  of  the  12 
games  that  they  played.  What  per  cent  of  games  did  they 
win? 

11.  A  girl  earned  $45.00  during  her  summer  vacation  and 
put  $28.80  of  that  amount  in  her  savings  account.  What  per 
cent  of  her  earnings  did  she  put  in  her  savings  account? 

12.  A  merchant  sold  eggs  which  cost  him  36  cents  a  dozen  at 
40  cents  a  dozen.  What  was  his  per  cent  of  profit?  What 
would  have  been  his  per  cent  of  profit  at  42  cents  per  dozen? 


190  EIGHTH  YEAR 

13.  An  agent  bought  an  automobile  for  $800  and  sold  it  for 
$1120.    What  was  his  per  cent  of  profit? 

14.  A  cubic  foot  of  wrought  iron  weighs  489  pounds.  A 
cubic  foot  of  water  weighs  62.5  pounds.  Water  is  what  per  cent 
as  heavy  as  wrought  iron? 

Exercise  29 

1.  Sea  water  contains  approximately  3%  of  salt.  How  much 
sea  water  must  be  evaporated  to  obtain  12  pounds  of  salt? 

2.  A  farmer  sold  45  hogs,  which  were  Q2^%  of  his  total 
number  of  hogs.    How  many  hogs  did  he  have  left? 

3.  Butter  fat  constitutes  85%  of  the  weight  of  butter. 
How  many  pounds  of  butter  can  be  made  from  6.8  pounds  of 
butter  fat  which  is  contained  in  a  can  of  cream? 

4.  A  horse  buyer  sold  a  horse  for  $161  at  a  profit  of  15%. 
Find  the  cost  of  the  horse. 

6.  A  dressed  steer  weighed  877.5  pounds.  This  was  only 
65%  of  its  live  weight.    What  was  the  live  weight  of  the  steer? 

6.. The  weight  of  a  cubic  foot  of  water  (62.5  pounds)  is 
5.18%  of  the  weight  of  a  cubic  foot  of  gold.  Find  the  weight 
of  a  cubic  foot  of  gold. 

7.  A  merchant  sold  a  suit  of  clothes  for  $28  at  a  gain  of 
40%.    Find  how  much  the  merchant  paid  for  the  suit. 

8.  A  firm  increased  the  wages  of  its  employees  10%.  What 
was  the  previous  salary  of  a  man  who  is  receiving  $132  under 
the  new  schedule? 

9.  The  number  of  girls  in  a  class  is  21.  If  the  girls  comprise 
60%  of  the  membership  of  the  class,  find  the  total  number  in 
the  class. 

10.  A  basket  ball  team  won  80%  of  its  games  during  a  certain 
year.    If  it  won  12  games,  how  many  games  did  it  play? 


REVIEW  EXERCISES— INTEREST  191 

INTEREST 
Exercise  30 

1.  Find  the  interest  on  $750  for  1  year  3  months  and  18 
days  at  6%. 

2.  Find  the  interest  on  $5000  for  10  months  and  12  days  at 

5%. 

3.  A  milliner  has  a  certificate  of  deposit  from  a  bank  for 
$350.  The  bank  pays  her  3%  interest  on  that  amount  if  she 
leaves  it  in  the  bank  more  than  3  months.  What  was  her 
interest  for  6  months? 

4.  A  merchant  borrowed  $2500  from  a  loan  company  for 
3  years  at  6%.    What  was  his  yearly  interest  payment? 

5.  A  farmer  bought  a  farm  for  $12,500.  He  made  a  cash 
payment  of  $4500.  He  borrowed  $6000  from  an  insurance 
company  at  5^%  and  gave  the  owner  his  note  for  the  remainder 
at  6%  interest.  What  was  the  total  of  his  interest  payments 
per  year? 

6.  A  school  district  issued  twenty  $1000  (one-thousand- 
dollar)  bonds  bearing  5%  interest,  one  of  the  bonds  being  paid 
off  at  the  end  of  each  year.  What  was  the  interest  on  these 
bonds  the  first  year? 

7.  How  much  was  the  interest  decreased  each  year  by  paying 
off  one  of  the  bonds? 

8.  Find  the  total  interest  paid  on  the  twenty  bonds  before 
they  were  all  paid  off? 

9.  The  interest  from  a  certain  note  for  one  year  at  6% 
amounted  to  $72.    Find  the  face  of  the  note. 

10.  The  interest  on  a  note  for  $400  for  6  months  was  $14. 
Find  the  rate  of  the  interest. 

11.  Find  the  interest  on  $250  for  3  yeats  6  months  at  6%. 


192  EIGHTH  YEAR 

COMMISSION 
Exercise  31 

1.  A  lawyer  charged  5%  for  collecting  debts  for  a  grocer, 
amounting  to  $1375.    What  was  his  fee? 

2.  A  salesman  received  a  salary  of  $1200  per  year  and  a 
commission  of  2%  on  his  sales.  What  was  his  total  income  for 
the  year  if  his  sales  amounted  to  $40,000? 

3.  A  commission  firm  sold  a  carload  of  196  barrels  of 
Black  Twig  apples  at  $3.50  per  barrel.  What  was  their  com- 
mission at  7%  on  the  sales? 

4.  A  commission  firm  bought  $36,500  worth  of  cotton  for 
a  factory.  What  was  the  amount  of  their  commission  at  2%? 
Find  the  total  cost  of  the  cotton  to  the  firm. 

6.  A  commission  firm  sold  300  baskets  of  Concord  grapes 
at  18  cents  each  and  remitted  $50.22  to  the  owner.  Find  the 
rate  of  their  commission. 

6.  A  real  estate  dealer  sold  a  farm  of  160  acres  at  $125  per 
acre  on  a  commission  of  2%.  What  was  the  amount  of  his 
commission  on  the  transaction? 

7.  A  collector  charged  5%  commission  for  collecting  a 
debt  of  $1500.    How  much  should  he  remit  to  the  creditor? 

8.  A  real  estate  dealer  sold  5  city  lots  at  $2500  each,  charg- 
ing 3%  commission.    Find  his  commission  on  the  5  lots. 

9.  What  was  a  broker's  commission  for  selling  1600  bushels 
of  wheat  at  f  jii  per  bushel? 

10.  An  agent  received  $2.50  commission  on  an  article  which 
he  sold  at  $9.60.    Find  his  rate  of  commission. 

11.  A  real  estate  agent  sold  a  farm  at  a  commission  of  5%. 
If  he  received  $500  for  his  commission,  what  was  the  selling 
price  of  the  farm?    How  much  did  he  remit  to  the  owner? 


REVIEW  EXERCISES— DISCOUNTS  193 

DISCOUNTS 
Exercise  32 

1.  A  certain  ice  company  sells  a  1250-pound  ice  ticket  for 
$4.00.  A  discount  of  25  cents  is  allowed  from  this  price  if  it 
is  paid  for  within  10  days.  What  is  the  per  cent  allowed  for 
prompt  payment? 

2.  My  gas  bill  for  the  month  of  January,  1917,  was  $1.98. 
A  discount  of  22  cents  is  allowed  if  the  bill  is  paid  within  10 
days.    Find  the  per  cent  of  discount  for  prompt  payment. 

3.  A  school  bought  a  dozen  jack  planes  listed  at  $36.00 
per  dozen.  It  was  allowed  the  regular  discount  of  20%  and 
an  extra  discount  of  2%  for  cash.  What  as  the  net  cost  of 
the  dozen  planes? 

4.  A  furniture  store  advertised  a  discount  of  20%  on  all 
furniture  during  the  month  of  July.  What  was  the  sale  price 
on  a  library  table  formerly  listed  at  $24.00? 

6.  A  retail  dealer  bought  a  piano  listed  at  $500  with  dis- 
counts of  20%  and  15%.    What  was  the  net  price  of  the  piano? 

6.  Which  is  better  for  a  retail  dealer,  discounts  of  20% 
and  15%  or  a  single  discount  of  33^%? 

7.  A  merchant  marked  dress  goods  costing  $1.20  per  yard 
to  sell  at  a  profit  of  50%.  During  a  clearance  sale  he  discounted 
the  marked  price  25%.  Find  his  sale  price  per  yard  on  the 
dress  goods. 

8.  A  hardware  firm  bought  a  bill  of  goods  amounting  to 
$1345.40.  They  were  allowed  a  discount  of  2%  for  prompt 
payment.    What  was  their  net  bill? 

9.  A  dealer  sold  straw  hats  of  a  certain  grade  for  $3.00 
early  in  the  season.  Late  in  the  season  he  sold  them  at  a 
clearance  sale  for  $1.80.  Find  the  per  cent  of  discount  which 
he  gave  on  this  sale. 


194  EIGHTH  YEAR 

TAXES 
Exercise  33 

1.  The  tax  rate  for  a  rural  school  district  was  $.79  per  $100 
of  valuation.    $.79  is  what  decimal  fraction  of  $100? 

2.  What  was  the  total  amount  raised  in  taxes  for  this  dis- 
trict if  the  total  valuation  of  the  district  was  $84,643? 

3.  In  a  certain  state  the  assessed  valuation  of  property  is 
taken  as  ^  of  the  full  value.  If  I  own  a  house  and  lot  valued 
at  $3600,  what  will  be  my  assessed  valuation  on  the  place? 

4.  If  the  total  tax  rate  is  $4.35  per  $100,  what  will  be  the 
taxes  on  this  house  and  lot? 

.  6.  The  state  tax  on  this  property  amounted  to  80  cents  per 
$100.    Find  the  amount  of  state  tax  on  the  house  and  lot. 

6.  The  school  tax  on  this  property  was  $1.95  per  $100. 
Find  the  amount  of  the  school  tax. 

7.  The  valuation  in  a  certain  county  was  $32,450,000  and 
the  amount  levied  for  taxes  in  a  certain  year  was  $120,000. 
Find  the  approximate  rate  per  $100  of  taxable  property. 

8.  A  single  woman  schedules  her  income  as  follows:  Divi- 
dends from  stock,  $2500;  rent  from  farm,  $1020;  rent  on  city 
residence,  $360;  miscellaneous  sources,  $500.  What  was  her 
income  tax?     (See  page  116 .) 

9.  A  town  having  property  valued  at  $350,000  made  a 
special  assessment  of  3  mills  on  the  dollar^  for  library  purposes. 
What  was  the  amount  raised  for  library  purposes? 

10.  A  county  made  a  special  assessment  of  2  mills  on  the 
dollar  for  good  roads.  How  much  taxes  were  raised  if  the 
valuation  of  the  county  was  $28,372,480? 

'A  rate  of  3  mills  on  the  dollar  reduced  to  a  decimal  =  .003  of  the  assessed 
valuation. 


REVIEW  EXERCISES— INSURANCE  195 

INSURANCE 

Exercise  34 

1.  How  much  must  I  pay  to  insure  my  household  goods  val- 
ued at  $500  at  a  rate  of  42  cents  per  $100? 

2.  The  premium  on  a  house  worth  $3000,  insured  at  80% 
of  its  value,  was  $15.60.    Find  the  rate  of  insurance  per  $100. 

3.  A  grocer  insured  his  stock  of  goods  valued  at  $2000  at 
80%  of  their  value  at  a  premium  of  1%  for  3  years.  What  was 
the  amount  of  his  premium? 

4.  A  school  house  cost  $40,000.  It  was  insured  at  80%  of 
its  value  at  a  premium  of  1  j%  for  3  years.  Find  the  amount 
of  the  premium. 

5.  A  lawyer  took  out  an  ordinary  life  insurance  policy  for 
$5000  at  the  age  of  30.  The  rate  in  his  company  at  that  age 
was  $19.74  per  thousand.     What  was  his  annual  premium? 

6.  The  agent  securing  the  policy  received  a  commission  of 
50%  of  the  first  premium.  What  was  the  agent's  commission 
on  the  $5000  policy? 

7.  Why  should  an  inventory  of  household  goods  be  made  out 
before  they  are  insured? 

8.  A  man  carried  insurance  on  his  household  goods  for 
$1000  at  the  rate  of  40  cents  per  $100.  He  paid  this  rate  for 
10  years.    How  much  did  his  insurance  cost  him? 

9.  During  the  tenth  year  his  house  was  burned  and  his 
household  goods  were  a  total  loss.  The  inventory  of  his  goods 
showed  that  their  value  was  really  only  $700  and  he  received 
that  amount  in  the  adjustment  with  the  insurance  company. 
Since  he  had  paid  insurance  on  $1000,  how  much  insurance  did 
he  pay  from  which  he  received  no  returns? 

10.  If  I  pay  a  premium  of  $37.50  on  a  house  insured  at 
$3000,  what  is  the  rate  per  $100? 


196  EIGHTH  YEAR 

APPROXIMATION  PROBLEMS 

Exercise  35 

Many  problems  actually  arising  in  life  are  not  solved  at 
once  with  exactness,  but  only  approximately.  The  habit  of 
inspecting  a  problem  and  roughly  estimating  the  answer 
(in  advance)  is  of  value  in  preventing  the  danger  of  being 
satisfied  with  an  absurdly  incorrect  result. 

1.  A  man  owes  the  following  amounts:  $173.57,  $54.55, 
$46.10  and  $198.28.    Does  he  owe  more  or  less  than  $500? 

2.  I  can  save  from  my  wages  $3.50  per  day.  Working  26 
days  per  month,  about  how  long  will  it  take  me  to  save  $1000? 

3.  A  fruit  ranch  yields  2600  boxes  of  peaches  which  sell 
at  48  cents  the  box.    Will  the  receipts  exceed  $1300? 

4.  4000  boxes  of  apples  bring  $1.14  per  box.  Will  the 
proceeds  exceed  or  be  less  than  $5000? 

6.  I  have  borrowed  $1385  for  one  year  at  8%.  Shall  I 
pay  more  or  less  than  $100  interest? 

6.  A  man  purchased  a  house  for  $6100,  and  sold  it  later 
for  $6800.    Did  he  gain  more  or  less  than  10%? 

7.  Give  the  approximate  cost  of  16  dozen  eggs  at  38  cents. 

8.  Give  the  interest  for  one  year  on  $990  at  6%. 

9.  Give  the  income  from  $22,240  at  6%;  7%;  11%. 

10.  What  is  9%  of  6,500,000?    Is  it  58,500  or  585,000? 
Give  the  approximate  results  of  the  following : 

11.  50X49?     1100-^50.4?    18,527+1460?     527+110+92? 

12.  Is  6,521,865   divided  by  276   about   2000  or   20,000? 

13.  What  is  the  distance  covered  by  an  automobile  in  21 
hours  when  averaging  18  f  miles  per  hour? 

14.  The  assessed  valuation  of  a  school  district  is  $21,945,865. 
The  expenses  of  conducting  the  schools  are  $112,000.  What 
is  the  approximate  rate  of  taxation  for  school  purposes? 


APPROXIMATION  PROBLEMS  197 

Exercise  36 

Not  only  should  approximations  be  used  for  checking  the 
more  accurate  solutions  of  problems  but  a  shortening  of  the 
work  may  also  be  accomplished  and  an  approximation  be  ob- 
tained which  is  very  near  the  accurate  result.  These  approxi- 
mations may  be  used  in  all  solutions  where  extreme  accuracy 
is  not  demanded. 

1.  Multiply  54.3725  by  28.213. 

Regular  form  Short  form 

54.3725  54.4 

28.213  28.2 

1631175  .  1088 

543725  4352 

1087450  1088 

4349800  1534.08 

1087450 


1534.0113425 


In  the  short  form  the  nearest  tenth  is  taken  (.37  being  nearest 
.4  and  .21  being  nearest  .2).  The  problem  (54.4  X  28.2)  con- 
tains 3  partial  products  instead  of  5  partial  products  in  the  com- 
plete multiplication  and  shows  a  very  material  saving  in  both 
multiplication  and  addition. 

In  a  similar  way  find  the  approximate  results  by  the  short 
form : 

2.  19.493  X  65.6125.  7.  984.5738  X  86.7245 

3.  3.1416  X  49.375  8.  708.3185  X  94.8732 

4.  1.4142  X  69.875  9.  830.5693  X  64.4286 
6.  32.5862  X  246.243  10.  958.0136  X  75.8316 
6.  42.325  X  86.4824                11.  804.9125  X  16.7854 

12.  A  rectangle  is  11.875  inches  long  and  9.625  inches  wide. 
Find  the  approximate  area  in  square  inches. 

The  area  of  a  rectangle  equals  the  length  multiplied  by  the  width. 


198  EIGHTH  YEAR 

Exercise  37 

Where  extreme  accuracy  is  not  demanded  in  division,  approx- 
imate results  may  be  secured  by  abridging  the  results. 
1.  Divide  84738  by  8754. 


Complete  Division 
9.680+ 

Abridged  Division 
9.680+ 

8754)84739.000 

78786 

8754)84739. 
78786 

59530 
52524 

5953 
5250 

70060 
70032 
280 

703 
696 

7 

In  the  abridged  form  of  division  instead  of  adding  a  zero  to 
the  dividend  and  carrying  the  decimal  part  of  the  quotient  out 
exactly,  a  figure  is  cancelled  off  the  divisor  and  the  multipHca- 
tions  and  subtractions  are  shortened. 

Divide  the  following  with  the  abridged  form : 

2.  19864  -4-  5280  5.  8500  -i-  1760  8.  39284  -^  6528 

3.  50875  -f-  31416         6.  14500  -^  1728  9.  80565  -^  9275 

4.  35  ^  5236  7.  1728  4-  231  10.  64258  ^  5162 

11.  53186  -i-  7854 
In  pointing  off  the  quotients  in  division  problems  containing 
decimals  an  approximation  should  always  be  made  as  a  check, 

12.  In  dividing  82.5  by  1.92,  thmk  about  80  ^  about  2. 
What  is  the  approximate  result? 

13.  In  dividing  625  by  .875  will  the  quotient  be  more  or  less 
than  625? 

14.  What  is  the  approximate  quotient  obtained  by  dividing 
78.45  by  3.1416? 

16.  In  dividing  a  number  by  ,1  the  quotient  will  be  how 
many  times  as  great  as  the  dividend? 


CHAPTER  II 
BANKS  AND  BANKING 


Interior  of  a  Large  City  Bank 

Banks  perform  various  services  for  us.  Among  the  most  im- 
portant of  these  services  are:  (1)  they  receive  money  on  de- 
posit for  safe  keeping  and  hold  it  subject  to  checks;  (2)  they  loan 
money  on  promissory  notes;  (3)  they  buy  at  a  discount  notes  and 
other  transferable  forms  of  commercial  paper;  (4)  they  act  as 
mediums  of  exchange  between  individuals  and  firms  in  different 
cities;  and  (5)  certain  banks  issue  paper  money. 

Opening  an  Account  in  a  Bank 

When  you  wish  to  open  an  account  in  a  bank,  you  should 
fill  out  a  deposit  slip  similar  to  the  one  on  the  next  page  and  sign 
your  name  to  it.  The  bank  will  then  have  your  signature  to 
compare  with  the  signature  on  your  checks. 

199 


200 


EIGHTH  YEAR 


FARMERS*  NATIONAL  BANK 


DEPOSITED  TO  THE  CREDIT  OF 


,N. ...  QJvdl/ G  ^a^f. 


Fort  DEARBOR^ 
(checks  are  received  for  collection) 


DRAFTS      ... 

Q>8  20 

CHECKS            .... 

i3 

GS 

CURRENCY         .... 

G 

^0 

TOTAL 

118 

.Z5 

should  always  be  taken  to  the  bank 
are  made. 

Exercise  1 


In  filling  out  this 
deposit  slip  you  must 
indicate  the  various 
items  which  make  up 
the  whole  deposit. 
This  is  done  for  the 
convenience  of  the  re- 
ceiving teller  of  the 
bank  who  checks  the 
amounts  which  you 
have  placed  on  your 
deposit  slip  to  see  if 
they  are  correct.  If  he 
finds  the  total  correct 
he  places  this  amount 
to  your  credit  in  a 
small  bank  book  upon 
which  he  writes  your 
name.  This  bank  book 
when  additional  deposits 


1.  Make  a  deposit  shp  similar  to  the  form  given  and  fill 
out  the  deposit  slip  for  John  Smith  for  the  following  items: 
a  draft  for  $50.00;  three  checks  for  $7.50,  $3.75,  and  $14.25; 
and  the  following  amount  of  money:  2  ten-dollar  bills;  7  five- 
dollar  bills;  13  one-dollar  bills;  11  haK-doUars;  17  quarters; 
22  dimes;  31  nickels;  48  pennies. 

2.  Write  a  deposit  slip  for  Richard  Roe  on  a  deposit  slip 
secured  from  one  of  the  local  banks.  Turn  in  a  list  of  the  kinds 
of  money,  etc.,  as  shown  in  Problem  1.  (It  will  be  more  con- 
venient for  the  teacher  to  secure  the  blank  forms  from  a  bank 
for  class  use.) 


BANKS  AND  BANKING.    CHECKS 
Checking  against  Your  Account 


201 


Check  books  with  blanks  which  can  be  easily  and  rapidly 
filled  out  are  supplied  by  the  banks.  They  contain  stubs  from 
which  the  checks  may  be  torn.  These  stubs  contain  blank 
spaces  for  the  amount  of  the  check,  the  number  of  the  check, 
the  date  issued,  to  whom  the  check  was  issued,  and  for  what  it  was 
written 


^oXi&jM  ^I 


%7zi 


^jb  ji/vevJ/u-'  oU 


'Mrty  r-    Yioo 


'9,00 


e.  ^^ockhu 


Stub 


Check 


The  above  illustration  shows  a  check  and  its  corresponding 
stub  properly  filled  out.  Note  that  the  amount  of  the  check 
in  figures  is  written  close  to  the  dollar  sign  and  the  amount  in 
words  is  written  at  the  extreme  left  end  of  the  line  and  the  space 
at  the  right  filled  in  with  a  fine.  These  precautions  should  al- 
ways be  taken  to  prevent  any  dishonest  person  from  putting  in 
extra  figures  and  prefixing  extra  words  and  thus  "raising"  the 
amount  of  the  check.  The  stubs,  if  properly  filled  out,  form  a 
record  of  all  money  paid  out  and  can  be  used  to  check  the 
monthly  statement  of  your  account  which  is  sent  by  the  bank. 
The  returned  checks  may  serve  as  receipts  for  bills  paid. 

Exercise  2 

1.  To  whom  was  the  above  check  issued?    By  whom  was  it 
written?    For  what  purpose  was  it  issued? 

2.  Write  a  check  for  $25.40  to  John  Doe  and  sign  your 
own  name.     (Secure  blank  checks  from  a  bank  for  this  work.) 


202  EIGHTH  YEAR 

The  person  who  presents  the  check  to  the  paying  teller, 
to  be  "cashed,"  must  indorse  it.  This  is  done  by  writing 
his  name  on  the  back  of  the  check,  as  shown  below  :^ 


If  the  depositor  makes  a  check  payable  to  himself  and  indorses 
it,  any  one  may  present  it  for  payment.  If  he  makes  it  payable 
to  some  particular  person,  that  person  (called  the  'payee) 
must  indorse  it,  whether  he  transfers  it  to  any  one  else  or  pre- 
sents it  for  payment  at  the  bank. 

Checks  should  be  presented  promptly  for  pa3nnent.  "When 
checks  are  received  by  a  bank  for  deposit,  they  are  credited 
as  cash,  for  they  are  immediately  collected  from  the  banks 
on  which  they  are  drawn. 

3.  If  you  receive  a  check  made  payable  to  yourself  and 
you  lose  it  before  you  have  indorsed  it,  can  the  finder  cash  it 
at  the  bank  without  forging  your  name? 

4.  If  you  receive  a  check  made  payable  to  yourself  and 
you  indorse  it  and  then  lose  it,  can  the  finder  cash  it  at  the 
bank? 

6.  If  you  receive  a  check  made  payable  to  "bearer,"  can 
any  one  cash  it  at  the  bank  without  your  indorsement  of  it? 
Is  it  best  to  make  checks  in  this  way? 

6.  If  in  sending  a  check  you  indorse  it  with  an  order  to  pay 
a  certain  person  (giving  his  name),  can  any  other  person  who 
finds  it  cash  it? 

'An  indorsement  should  be  on  the  back  of  the  left  end  of  the  check 
at  least  one  inch  from  the  end. 


BANKS  AND  BANKING— CHECKS 

A  check  so  indorsed  is  said  to  be  "indorsed  in  full." 
An  Indorsement  in  Full 


203 


7.  If  you  receive  a  check  made  payable  to  yourself,  and  if, 
instead  of  presenting  it  personally  at  the  bank,  you  send  it  to 
another  person  with  the  mere  indorsement  of  your  name 
(which  is  called  an  indorsement  in  blank),  and  it  is  lost  in 
transit,  can  any  finder  of  it  cash  it? 

8.  Write  a  check  for  a  fictitious  amount  to  be  paid  to  John 
Doe,^  and  sign  the  name  Richard  Roe. 

9.  Write  a  check  for  a  fictitious  amount  to  be  paid  to 
Richard  Roe,  and  sign  the  name  John  Doe. 

10.  Indorse  in  blank  the  check  written  in  Problem  8  above. 

11.  Indorse  in  full  the  check  in  Problem  9,  using  any  other 
fictitious  name. 

12.  On  a  check  made  by  John  Doe  to  himself,  write  an 
indorsement  in  full,  authorizing  payment  to  Richard  Roe. 

The  use  of  checks  renders  it  easy  to  pay  bills  by  mail,  and 
in  various  ways  it  lessens  the  risk  of  loss  in  the  transmission 
of  money. 

At  stated  periods,  usually  at  the  close  of  each  month,  the 

paid  checks  are  returned  by  banks  to  the  persons  who  issued 

them;  and  they  thus  serve  as  receipts,  since  they  show  that 

the  moneys  have  been  paid. 

'"John  Doe"  and  "Richard  Roe"  have  been  for  centuries  legal  desig- 
nations for  supposititious  or  unknown  personages. 


204 


EIGHTH  YEAR 


Savings  Accounts 

State  banks  usually  have  savings  departments  in  which 
they  pay  a  small  rate  of  interest  (usually  3%  or  4%)  on  savings 
deposits.  One  dollar  is  usually  required  for  opening  a  savings 
account. 

When  the  interest  is  due,  it  is  added  to  the  depositor's  account 
and  draws  interest  the  same  as  the  original  deposits.  The 
following  quotation  from  a  savings  account  book  shows  their 
method  of  computing  interest: 

"Interest  will  be  allowed  from  the  first  day  of  the  month  following  the 
deposit,  except  that  deposits  made  up  to  the  5th  of  any  month  shall  be 
considered  as  being  made  upon  the  first  day  of  the  month,  and  wiU  draw 
interest  accordingly.  Interest  will  be  computed  on  the  first  days  of  Janu- 
ary and  July  of  each  year  on  all  sums  then  on  deposit,  at  the  rate  of  three 
per  cent  per  annum  on  all  savings  deposits  which  have  remained  on  deposit 
for  one  month  or  more,  but  interest  wiU  not  be  allowed  upon  fractional 
parts  of  a  dollar,  nor  for  fractional  parts  of  a  month,  nor  on  any  sum  with- 
drawn between  interest  days,  for  any  of  the  periods  which  may  have 
elapsed  since  the  preceding  interest  day.  All  withdrawals  between  interest 
days  will  be  deducted  from  the  first  deposit." — Woodlawn  Trust  and 
Savings  Bank. 

Form  of  a  Savings  Account 


Date 

Teller 

Withdrawals 

Deposits 

Balance 

7/  2/16 

W 

$100 

$100 

8/15/16 

W 

50 

150 

10/  1/16 

W 

30 

180 

10/30/16 

W 

$20 

160 

11/26/16 

W 

10 

170 

Exercise  3 

1.  Compute  the  interest  on  the  above  savings  account  for 
the  interest-paying  date  Jan.  1,  1917,  according  to  the  rules 
given  in  the  quotation  from  the  Woodlawn  Trust  and  Savings 
Bank. 


BANKS  AND  BANKING— INTEREST 


205 


2.  If  there  were  no  deposits  or  withdrawals  between  Jan.  1, 
1917,  and  July  1,  1917,  what  would  be  the  balance  on  the 
latter  date? 

Compound  Interest 

If,  when  due,  the  simple  interest  is  added  to  the  principal 
to  form  a  new  principal  for  the  next  interest  period  and  this 
process  is  repeated  during  all  the  interest  periods  of  the  loan, 
the  difference  between  the  final  amount  and  the  original  prin- 
cipal is  called  compound  interest. 

From  the  preceding  exercise  it  is  seen  that  savings  banks 
make  use  of  compound  interest.  The  calculation  of  compound 
interest  for  any  considerable  length  of  time  involves  so  many 
steps  that  it  is  generally  avoided  by  the  use  of  a  Compound 
Interest  Table.  The  following  table  shows  the  amount  of  one 
dollar  for  twenty  annual  interest  periods: 


Table  showing  amount  op  $1.00  at  compound  interest,  extended  to  rnm 

DECIMALS  FOB  EACH  OP  TWENTY  PERIODS  PROM  1  TO  7  PER  CENT. 


1 

2 

3 

4 

5 

6 

7 

Year 

Per  Cent 

Per  Cent 

Per  Cent 

Per  Cent 

Percent 

Per  Cent 

Per  Cent 

1 

1.01000 

1.02000 

1.03000 

1.04000 

1.05000 

1.06000 

1.07000 

2 

1.02010 

1.04040 

1.06090 

1.08160 

1.10250 

1.12360 

1.14490 

3 

1.03030 

1.06121 

1.09273 

1.12486 

1.15763 

1.19102 

1.22504 

4 

1.04060 

1.08243 

1.12551 

1.16986 

1.21551 

1.26248 

1.31080 

5 

1.05101 

1.10408 

1.15927 

1.21665 

1.27628 

1.33823 

1.40255 

6 

1.06152 

1.12616 

1.19405 

1.26532 

1.34010 

1.41852 

1.60073 

7 

1.07213 

1.14869 

1.22987 

1.31593 

1.40710 

1.50363 

1.60578 

8 

1.08286 

1.17166 

1.26677 

1.36857 

1.47746 

1.59385 

1.71819 

9 

1.09368 

1.19509 

1.30477 

1.42331 

1.55133 

1.68948 

1.83846 

10 

1.10462 

1.21899 

1.34392 

1.48024 

1.62889 

1.79085 

1.96715 

11 

1.11567 

1.24337 

1.38423 

1.53945 

1.71034 

1.89830 

2.10485 

12 

1.12682 

1 . 26824 

1.42576 

1.60103 

1.79586 

2.01220 

2.25219 

13 

1.13809 

1.29361 

1.46853 

1.66507 

1.88565 

2.13293 

2.40985 

14 

1.14947 

1.31948 

1.51259 

1.73168 

1.97993 

2.26090 

2.57853 

15 

1.16097 

1.34587 

1.65797 

1.80094 

2.07893 

2.39656 

2.75903 

16 

1.17258 

1.37279 

1.60471 

1.87298 

2.18287 

2.54035 

2.95216 

17 

1.18430 

1.40024 

1.65285 

1.94790 

2.29202 

2.69277 

3.15882 

18 

1.19615 

1.42825 

1.70243 

2.02582 

2.40662 

2.85434 

3.37993 

19 

1.20811 

1.45681 

1.75351 

2.10685 

2.52695 

3.02560 

3.61653 

1    20 

1.22019 

1.48595 

1.80611 

2.19112 

2.65330 

3.20714 

3.86968 

206  EIGHTH  YEAR 

The  preceding  table  is  made  out  for  annual  payments.  For  semi- 
annual periods  take  half  the  rate  for  double  the  number  of  years.  For 
example:  to  find  the  compound  amount  on  $1  at  6%  for  10  years 
compounded  semi-annually  find  the  amount  in  the  table  for  3%  for 
20  years.  The  compound  interest  is  the  difference  between  the  com- 
pound amount  and  the  original  principal. 

Exercise  4 

1.  Find  by  the  table  the  compound  amount  of  $1000 
at  6%  for  ten  years,  payable  annually. 

2.  Find  the  compound  interest  of  the  same. 

3.  How  much  greater  is  this  than  the  simple  interest  would 
be? 

4.  Find  by  the  table  the  compound  amount  of  $1000 
at  6%  for  ten  years,  payable  semi-annually? 

6.  How  much  greater  is  this  than  the  compound  amount 
of  the  same  principal  at  the  same  rate  per  cent,  the  interest 
being  paid  annually? 

6.  What  is  the  nearest  full  year  at  which  the  original 
principal  will  double  itself  at  compound  interest  at  6%,  payable 
annually? 

7.  What  is  the  nearest  full  year  at  which  the  original 
principal  will  treble  itself  at  compound  interest  at  6%,  payable 
annually? 

Some  banks  pay  4%.  interest  on  savings  deposits  but  usually 
require  that  the  money  be  left  on  deposit  at  least  one  year. 

8.  What  will  a  savings  deposit  of  $100  amount  to  in  8 
years,  compounded  semi-annually  at  4%? 

See  explanation  of  table  at  top  of  the  page. 

9.  Find  the  amount  of  a  savings  deposit  of  $300  in  10  years, 
compounded  semi-annually  at  4%. 


BANKS  AND  BANKING.     NOTES  207 

Borrowing  Money  at  a  Bank 

Since  the  depositors  do  not  often  check  out  their  entire  ac- 
counts or  all  of  them  present  checks  at  the  same  time,  banks  are 
only  compelled  to  keep  a  portion  of  their  deposits  on  hand  and 
may  loan  out  the  remainder. 


fsqaog_ ii:&.mimpJ3A9fWJl 

.^J^?^^.AIQ/UA^......    afterdate     U<_ promise,  to  pay  to  the 

..O^OOdi  .  .'f9P..SJ<dJ-fli\A'i.    for  value  received. 


A  Bank  Promissory  Note 

The  above  illustration  shows  one  form  of  a  bank  promissory 
note.  A  bank  usually  requires  the  person  who  borrows  the 
m^Sy  to  get  some  other  responsible  person  to  sign  the  note 
with  him.  If  the  signer  of  the  note  is  unable  to  pay  the  note, 
the  second  person  who  signed  the  note  as  security  is  held  re- 
sponsible for  its  payment.  Instead  of  getting  another  person 
to  go  on  the  note  as  security,  a  person  may  give  a  mortgage 
on  his  property  which  gives  the  bank  the  authority  to  sell  the 
property  in  the  event  that  the  signer  does  not  pay  the  note. 

In  this  type  of  note  the  bank  collects  the  principal  with  the 
accrued  interest  on  the  date  when  the  note  is  due. 

1.  Find  the  amount  due  on  the  above  note  when  it  is  due. 

2.  Find  the  amount  due  on  a  note  of  $1200  for  1  year 
at  6%  interest. 


208  EIGHTH  YEAR 

Bank  Discount 

Instead  of  loaning  money  on  a  promissory  note  bearing  inter- 
est, banks  sometimes  make  out  a  promissory  note  without  inter- 
est. They  then  deduct  interest  for  the  given  time  from  the 
face  of  the  note  and  the  borrower  receives  the  remainder. 

The  money  which  a  borrower  actually  receives  on  such  a  note 
is  called  the  proceeds  of  the  note.  The  interest  deducted  in 
advance  is  called  bank  discount. 

Bank  discount  differs  from  regular  interest  by  being  deducted  at  the 
beginning  of  the  discount  period  instead  of  being  added  at  the  date  of 
maturity. 


paa6asaaasaaaaaeesesa6S6S8^^^ssssss^iss^^s^s^^s^s^^^^ssssssssss6a(iBaeatta 


\a,:  6> 


Exercise  5 

1.  What  is  the  bank  discount  on  the  above  note? 

2.  What  are  the  proceeds  of  the  above  note? 

3.  Find  the  bank  discount  on  a  note  for  $450  for  60  days 
at  6%.    Find  the  proceeds. 

4.  What  is  the  bank  discount  on  $180  for  30  days  if  the  rate 
of  discount  is  6%? 

5.  If  you  give  a  bank  your  note  for  $250  for  90  days  at  6% 
discount,  what  proceeds  will  you  receive? 


BANKS  AND  BANKING.    EXCHANGE         209 

A  promissory  note  which  may  be  transferred  from  one  per- 
son to  another  by  being  indorsed  in  called  a  negotiable  note. 
Banks  frequently  buy  promissory  notes  from  persons  who  need 
the  money  before  the  notes  are  due.  In  such  cases  banks  dis- 
count the  amount  of  the  note  at  the  date  of  maturity  for  the 
time  between  the  date  of  discount  and  the  date  of  maturity. 

6.  A  bank  bought  a  note  for  $300  for  1  year  bearing  6% 
interest.  How  much  money  did  the  owner  of  the  note  receive 
if  the  period  of  the  discount  was  90  days  and  the  rate  of  the 
bank  discount  was  6%? 

7.  A  music  dealer  sold  a  phonograph  for  $275.  He  received 
a  note  for  that  amount  for  1  year  at  6%  interest.  He  dis- 
counted the  note  at  6%  the  same  day.     Find  the  proceeds. 

■Exchange 

One  of  the  most  important  functions  of  a  bank  is  the  payment 
of  debts  without  the  actual  transfer  of  money,  through  the 
interchange  of  checks  and  drafts. 

To  collect  a  debt  from  a  debtor  in  another  town  or  city, 
the  creditor  may  "draw"  on  him  for  the  amount  due.  This  is 
done  by  sending  to  a  bank  in  the  debtor's  home  town  or  city 
an  order  to  pay  the  amount.     This  order  is  called  a  draft. 

Generally  the  draft  is  sent  to  a  bank  with  which  the  debtor 
does  business.  The  draft  may  be  made  payable  to  the  creditor 
himself,  and  sent  to  the  bank  for  collection,  or  it^may  be  made 
payable  to  the  bank  itself.  The  order  is  addressed  directly 
to  the  debtor  drawn  upon,  the  address  being  written  generally 
in  the  lower  left  corner  of  the  paper. 

If  the  debtor  is  ordered  to  pay  the  draft  "at  sight,"  the 
paper  is  called  a  sight  draft.  If  the  order  calls  for  payment 
at  a  stated  later  time,  it  is  called  a  time  draft. 


210  EIGHTH  YEAR 

Sight  Draft 


At  sight  pay  to  the  order  of r^.-~^V. 

OmiL'J^^u/ndnjuL'  amcO  


for  value  received ,and  charge  the  same  to  the  account  of 


Cn<^ca^a^ 


JU. 


Time  Draft 


<SJu^...&Ci^f^„  ,ight,  pay  to  the  order  of  S^JmW^.T.^^^J^9/m'.... 
¥^^jSf^'^'^i:id^.9^1^^^  °^Oo}, _  for  value 


received  and  charge  to  tk^ 

sSo'./u'<Ji<l^  fkS/n/.&.Qii-. 


If  a  draft  is  a  time  draft,  the  bank  receiving  it  immediately 
presents  it  to  the  party  addressed  and  if  it  is  satisfactory  that 
party  writes  his  acceptance  and  the  date  across  the  face  as 
shown  in  the*above  illustration. 

A  check  drawn  by  one  bank  upon  another  is  called  a  "bank 
draft."  It  is  used  largely  to  avoid  the  needless  transmission 
of  actual  money  from  one  city  to  another.  The  cashier  signs 
for  the  bank  making  the  draft  ar  d  the  name  of  his  institution 
app)ears  at  the  top  of  the  paper,  as  on  a  letterhead,  while  the 
name  of  the  bank  drawn  upon  appears  below. 


BANKS  AND  BANKING— DRAFTS  211 

A  Bank  Draft 


hPMPO foAUidlu^ 

Pay  to  the  order  of ...p7l\/yV.^QP. 

Q^nsjjSJycru^^  

in  current  futids. 

...&.SmdjQ:imj,Jil, SaAfim>. 


The  banks  in  large  cities  have  a  clearing  house  where  each 
bank  presents  checks  and  drafts  which  they  have  cashed  for 
the  other  banks  in  the  city  and  only  the  balances  due  are  paid 
in  actual  currency.  Clearing  houses  in  central  banking  cities 
provide  for  the  exchange  of  checks  and  drafts  of  banks  in 
different  cities.  Balances  are  paid  in  clearing  house  certificates 
or  in  actual  currency. 

Where  the  obligations  of  the  business  houses  (including 
banks)  of  one  city  to  those  of  another  city  are  pretty  evenly 
balanced  by  obUgations  of  the  latter  to  the  former,  there  will 
be  no  occasion  for  the  transmission  of  cash  from  one  city  to 
the  other  for  the  settlement  of  the  obligations;  the  obligations 
of  the  business  houses  of  the  one  city  will  largely  cancel  those 
of  the  other,  and  this  ib  effected  by  the  use  of  drafts. 

If  the  business  houses  of  St.  Louis  owe  to  those  of  New  York 
a  large  surplus  over  the  indebtedness  of  New  York  to  St.  Louis, 
there  must  be  a  shipment  of  money  to  settle  the  balance.  Be- 
cause of  the  desire  to  avoid  the  actual  shipment  of  money, 
bank  drafts  on  New  York  will  be  sold  in  St.  Louis  at  a  sUght 
premium;^  while  drafts  on  St.  Louis  will  be  sold  in  New  York 
at  a  slight  discount. 

*A  premium  is  an  extra  amount  over  the  face  value.  The  premium  or 
discount  is  calculated  on  the  face  of  the  draft. 


212      ^  .  EIGHTH  YEAR 

According  to  the  condition  of  the  money  market,  drafts 
may  be  "at  par"  or  they  may  "appreciate"  or  "decline." 

Exercise  6 

1.  Write  a  sight  draft,  using  fictitious  names. 

2.  Write  a  time  draft,  using  fictitious  firms'  names. 

3.  Find  the  cost  of  a  sight  draft  for  $500  where  there  is 
in  the  money  market  a  premium  of  f  %. 

4.  Where  exchange  is  at  a  discount  of  J%,  what  will  be 
the  cost  of  a  sight  draft  for  $500? 

5.  What  is  the  cost  of  a  sight  draft  for  $1200  where 
exchange  is  at  a  premium  of  §%? 

6.  What  will  be  the  cost  of  a  sight  draft  for  $625  where 
exchange  is  at  a  discount  of  ^%? 

Time  Drafts 

In  the  case  of  time  drafts,  the  element  of  time  has  to  be 
taken  into  account.  The  bank  discount  for  the  time  specified 
is  deducted  from  the  face  of  the  draft,  and  the  premium,  or 
discount,  is  then  calculated  on  the  face  of  the  draft  and  added 
to  or  subtracted  from  the  remainder. 

Exercise  7 

1.  A  sixty-day  time  draft  for  $300  must  be  bought  where 
exchange  is  at  premium  of  f  %.    What  is  the  bank  discount? 

2.  What  can  be  obtained  for  a  draft  for  $400  payable  in 
90  days  from  sight,  and  discounted  at  the  time  of  its  acceptance? 
What  was  its  cost  at  a  discount  of  f  %? 

3.  What  must  I  pay  for  a  60-day  sight  draft  for  $600, 
the  premium  being  ^%,  discount  6%? 

4.  What  will  be  the  cost  of  a  draft  for  $1000  payable 
60  days  after  sight,  at  a  premium  of  J%,  discount  6%? 


^. 


BANKS  AND  BANKING  213 

How  a  Bank  Is  Organized 

When  a  group  of  men  wish  to  organize  a  bank,  they  first  decide 
upon  the  amount  of  capital  stock  which  they  wish  to  raise. 
They  then  sell  shares  for  $100  each  until  that  amount  of  capital 
stock  is  raised.  Then  they  have  a  meeting  of  the  owners  of 
the  stock  and  elect  a  board  of  directors.  In  this  meeting  each 
person  votes  in  proportion  to  the  number  of  shares  that  he 
owns.  The  board  of  directors  then  elect  the  officers  to  conduct 
the  actual  business  of  the  bank.  Before  the  bank  can  open  for 
business  a  charter  must  be  obtained  either  from  the  national 
government  or  from  the  state  government. 

National  banks  are  authorized  by  the  Secretary  of  the  Treas- 
ury and  are  inspected  by  national  officers  who  see  that  the 
business  is  conducted  in  compliance  with  the  regulations  of  the 
National  Banking  Act. 

National  banks  must  have  a  capital  of  at  least  $100,000, 
"except  that  banks  with  a  capital  of  not  less  than  $50,000  may, 
with  the  approval  of  the  Secretary  of  the  Treasury,  be  organ- 
ized in  any  place  the  population  of  which  does  not  exceed  6,000 
inhabitants." 

For  the  protection  of  their  depositors.  National  banks  are 
required  to  keep  on  reserve  at  least  12%  of  their  deposits. 
Experience  has  shown  that  this  is  sufficient  to  meet  the  daily 
withdrawals  by  depositors.  Part  of  this  reserve  may  be  de- 
posited in  certain  city  reserve  banks. 

Only  National  and  Federal  Reserve  banks  can  now  issue 
bank  notes  which  circulate  as  paper  money. 

Hundreds  of  years  ago  men  who  made  a  business  of  borrowing  and 
lending  money  had  benches  in  the  market  places  of  the  principal  cities 
and  drove  bargains  with  borrowers  and  lenders.  The  Italian  word  banco 
meant  bench  and  from  it  we  derive  our  word  bank.  When  one  of  the  old- 
time  bankers  failed,  his  bench  was  broken.  "Bankrupt,"  meaning  broken 
bench,  came  to  mean  a  debtor  who  could  not  pay. 


214  EIGHTH  YEAR 

Issuing  Bank  Notes 

National  banks  are  required  to  keep  on  deposit  with  the 
Secretary  of  the  Treasury  at  Washington,  government  bonds 
equal  to  one-fourth  of  their  capital  stock,  as  security  for  their 
circulating  bank  notes  which  they  may  issue  to  that  amount. 

If  a  national  bank  fails,  the  government  pays  the  bank  notes 
that  the  bank  has  in  circulation  from  the  sale  of  the  govern- 
ment bonds  which  had  been  deposited  to  secure  them.  The 
bank  notes,  then,  are  accepted  by  people  as  readily  as  the  gov- 
ernment paper  money  called  "greenbacks." 

Federal  Reserve  Banks 

National  banks  are  limited  in  issuing  bank  notes  to  one-fourth 
of  their  capital  stock.  There  are  times  when  the  business  inter- 
ests of  the  country  demand  more  money.  In  order  to  meet  this 
need  Congress  established  the  Federal  Reserve  banks^.  These 
banks  can  issue  bank  notes  to  meet  an  urgent  and  temporary 
need  for  more  money  and  then  withdraw  them  from  circulation 
after  the  emergency  is  past. 

Federal  Reserve  banks  are  to  be  found  in  only  twelve  large 
cities,  viz.:  New  York,  Chicago,  Philadelphia,  Boston,  St. 
Louis,  Cleveland,  San  Francisco,  Minneapolis,  Kansas  City, 
Atlanta,  Richmond,  and  Dallas. 

The  national  banks  are  all  required  to  be  members  of  a  Fed- 
eral Reserve  bank.  A  Federal  Reserve  bank  must  have  a  cap- 
ital of  $4,000,000  or  more.  Anyone  may  own  shares  in  a 
Federal  Reserve  bank,  but  only  a  member  bank  of  its  district 
is  permitted  to  own  at  any  one  time  more  than  $25,000  of  the 
capital  stock  of  one  of  these  banks. 

lA  Federal  Reserve  bank  is  essentially  "a  banker's  bank."  It  sus- 
tains with  its  members  much  the  same  relation  that  ordinary  banks 
sustain  with  their  depositors. 


BANKS  AND  BANKING  215 

Exercise  8 

1.  If  a  capitalist  owns  the  maximum  amount  permitted 
in  a  Federal  Reserve  bank  in  each  of  the  cities  named,  what  is 
the  par  value  of  his  investment? 

2.  What  was  the  minimum  capital  required  for  the  be- 
ginning of  business  by  the  12  Federal  Reserve  banks? 

3.  The  shares  of  stock  of  a  Federal  Reserve  bank  are  of 
the  par  value  of  $100  each.  How  many  shares  are  required 
to  be  taken,  to  amount  to  the  minimum  sum  required  for 
beginning  the  business  of  the  bank? 

4.  Three  state  banks  and  two  business  houses  each  purchase 
the  maximum  permitted  amount  of  stock  in  a  Federal  Reserve 
bank.     What  is  the  amount  of  their  stock  in  it? 

5.  If  a  certain  Federal  Reserve  bank  has  a  capital  of 
$20,000,000  and  yields  profits  of  6%  annually  on  the  capital 
stock,  what  will  be  the  amount  of  the  profits  that  may  be  dis- 
tributed in  one  year? 

State  banks  are  organized  under  state  laws  and  are  inspected 
by  state  officers.  A  smaller  amount  of  capital  stock  is  usually 
required  for  their  organization  than  for  a  national  bank. 

Trust  companies,  organized  under  state  laws,  not  only  con- 
duct a  banking  business  but  also  settle  estates,  take  care  of 
property  of  minors  (persons  under  legal  age),  and  perform 
various  other  services  not  permitted  in  state  or  national  banks. 

In  some  states  certain  individuals  or  partnerships  call  their 
offices  "private  banks,"  although  they  possess  no  bank  charters 
and  are  not  subject  to  any  official  inspection.  There  is  a  grow- 
ing demand  that  these  banks  be  placed  under  regular  state  in- 
spection to  protect  their  depositors. 

Make  a  study  of  the  various  kinds  of  banks  in  your  com- 
munity, noting  the  amounts  of  their  capital  stock,  total  depos- 
its, etc. 


216  EIGHTH  YEAR 

STOCKS  AND  BONDS 

Stocks 

To  a  very  great  extent  the  business  of  the  country  is  now 
conducted  by  corporate  companies,  called  corporations.  A 
corporation  is  regarded  in  law  as  an  artificial  person  created 
by  law  for  specified  purposes  and  having  specified  powers. 

/  The  capital  stock  of  a  corporation  is  divided  into  shares 
/  generally  having  a  face  or  par  value  of  $100  each  and  are 
I  usually  spoken  of  as  stocks. 

A  corporation  with  a  capital  stock  of  $50,000  has  500  shares 
of  $100  each  which  have  been  sold  to  different  individuals. 

All  who  own  any  of  the  stock  of  a  corporation  are  members 
of  it  and  have  votes  in  it  in  proportion  to  the  number  of  shares 
of  stock  which  they  possess. 

If  the  corporation  is  large  and  its  members  widely  scattered, 
the  members  elect  a  Board  of  Directors  to  manage  the  afifairs 
of  the  corporation. 

The  advantages  of  corporations  are:  (1)  They  enable  a  large 
amount  of  money  to  be  collected  from  small  investors  who 
would  not  be  able  to  invest  this  money  profitably  in  small 
amounts.  (2)  The  stockholders  of  a  corporation  are  subject 
to  a  Umited  liability  (usually  the  money  invested  in  the  stock) 
in  the  case  of  failure  in  the  business  of  the  corporation. 

In  a  partnership  or  an  unincorporated  company  each  person 
must  stand  responsible  for  the  debts  of  the  firm  and  even  his 
private  property  can  be  taken  to  pay  the  debts  of  the  firm. 

The  certifixxUes  of  stock  issued  to  the  members  of  a  corporation 
state  the  numbers  of  shares  held,  the  face  value  of  each  and 
how  the  stock  may  be  transferred. 

The  following  reproduction  illustrates  the  form  of  a  stock 
certificate: 


STOCKS  AND  BONDS— STOCKS 


217 


Stock  certificates  vary  somewhat  in  statement,  but  the  Common  Stock 
Certificates  are  usually  in  the  general  form  here  illustrated. 


Exercise  9 

1.  What  is  the  par  value  of  each  share  of  stock? 

2.  How  many  shares  of  stock  are  there  in  this  company? 

3.  In  what  state  was  this  company  incorporated? 

4.  How  may  the  stocks  in  this  company  be  transferred? 
Ji.  dividend  is  a  sum  received  for  each  share  when  all  or  a 

portion  of  the  profits  of  a  corporation  are  distributed  to  the 
shareholders. 

5.  If  the  dividends  of  the  Regal  Hat  Company  were  $5000, 
how  much  of  a  dividend  would  be  paid  on  each  of  the  500 
shares  ? 


218  EIGHTH  YEAR 

6.  The  dividend  of  $10  on  each  share  would  be  what  per 
cent  of  the  par  value  of  each  share? 

7.  Will  investors  be  anxious  to  buy  stock  that  is  paying 
10%  dividends  when  money  usually  only  yields  6%  interest? 

In  order  to  secure  stock  which  pays  a  high  dividend,  investors 
will  pay  more  than  the  par  value  of  the  stock.  They  may  pay 
$150  for  a  share  of  stock  whose  par  value  is  only  $100.  Such 
stock  would  be  quoted  as  worth  150  in  the  newspaper  report 
of  the  stock  exchange. 

The  following  were  among  the  items  in  the  report  of  a  daily 
paper  on  the  New  York  Stock  Exchange  for  Nov.  11,  1916: 

Sales'  High  Low  Close  Net  Change 

1.  Am.  B.  Sugar 2900   -  102^  101^  lOlf-  -§ 

2.  Am.  Exp 200  139|  136  139|  3^ 

3.  Am.  Wool 1000  53  52f  53  -  | 

4.  do.ipf 100  98  98  98  

5.  Beth.  Steel 200  670  665  665  -10 

6.  do.  pf 600  152  149  152  

We  see  from  the  above  sales  that  stocks  in  items  1,  2,  5  and  6 
are  selling  above  par.  Hence  those  companies  must  be  paying 
good  dividends  to  the  investors.  Items  3  and  4  show  those 
stocks  were  sold  below  par.  What  are  the  net  changes  in  each 
kind  of  stock  since  the  preceding  day? 

8.  Bring  to  the  class  for  study  extracts  of  the  stock  quo- 
tations in  the  daily  paper  showing  a  table  similar  to  the  above 
table. 

/Large  corporations  sometimes  issue  stock  of  two  kinds  or 
classes,  common  and  preferred  stock.  The  preferred  stock 
guarantees  that  all  dividends  up  to  a  certain  per  cent  of  the 
par  value  must  first  be  divided  among  the  holders  of  the  pre- 
ferred stock.  If  there  are  any  profits  left,  they  are  distributed 
among  the  holders  of  the  common  stock. 

'The  expression  do.  in  the  above  table  means  the  same  as  the  preceding 
Hem  and  thus  is  a  short  way  of  expressing  Am.  Wool  again. 


STOCKS  AND  BONDS— STOCKS  219 

The  stock  quotations  given  in  the  preceding  table  show  that 
the  preferred  stock  in  Item  4  is  more  valuable  than  the  common 
stock  in  Item  3.  That  corporation  then  is  not  doing  a  profitable 
enough  business  to  enable  sufficient  dividends  to  be  paid 
regularly  to  the  common  stock  holders.  In  Item  6  of  the  table, 
the  common  stock  is  selling  at  $670  per  share.  This  extremely 
high  price  was  caused  by  unusually  large  profits  coming  from 
the  manufacture  of  munitions  for  use  in  the  European  War. 
The  excess  profits  were  divided  as  shoAvn  above  among  the 
common  stock  holders,  thus  making  their  stock  much  more 
valuable  than  the  preferred  stock  in  that  company. 

The  amount  a  broker  receives  for  buying  and  selling  stock  is 
called  brokerage. 

In  buying  and  selling  stocks  the  hrolwrage  is  generally  f  % 
of  the  par  value  of  the  stocks.  When  stocks  are  bought,  the 
brokerage  is  added  to  the  market  price  to  find  the  total  cost. 
When  stocks  are  sold,  the  brokerage  is  taken  from  the  selling 
price  to  find  the  proceeds  due  the  owner  of  the  stock. 

If  the  class  can  secure  data  from  some  local  corporation, 
a  study  of  the  organization  of  this  local  company  will  prove  a 
valuable  exercise. 

Exercise  10 

1.  If  a  gas  and  electric  company,  incorporated,  pajrs 
quarterly  dividends,  two  of  them  being  3%  and  two  of  them 
2%,  what  income  is  derived  annually  from  10  shares,  of  $100 
each? 

2.  What  will  be  the  cost  of  100  shares  of  stock  of  a  certain 
railway  (par  value  $100)  if  you  buy  them  at  125%  and  pay 
\%  brokerage? 

Solution:    125%+J%  =  125|%. 

125j%X $100  =  $125,125,  cost  of  1  share. 
100  X  $125. 125  =  $12,512.50,  cost  of  100  shares. 


220  EIGHTH  YEAR 

3.  A  broker  sells  200  shares  ot  American  Express  stock  at 
139 i%>  brokerage  |%.  Find  the  amount  of  the  proceeds 
which  he  sends  the  previous  owner  of  the  stocks. 

Solution:    139i%-i%  =  139i%,  proceeds  from  1  share. 

139|%X$100  =  $139.125,  proceeds  from  1  share. 
200X139.125  =  $27,825.00,    proceeds    from    200 
shares. 

4.  A  broker  sells  500  shares  of  American  Wool  preferred  at 
98,  brokerage  ^%.  What  is  the  amount  of  the  proceeds  which 
he  sends  his  principal? 

6.  If  money  is  worth  5%,  what  must  be  the  dividends  from 
one  share  of  the  Bethlehem  Common  Steel  in  order  for  it  to 
sell  for  670?    What  per  cent  of  the  par  value  is  this? 

Solution: 
5%  X  $670  =  $33.50,  amount  of  dividends  on  one  share. 
$33.50  =  X%X  $100. 
X%  =  ^=  .335  or  33.5%,  per  cent  of  par  value. 

6.  If  money  is  worth  5%,  what  will  be  the  market  quotation 
for  stocks  of  good  security  paying  an  annual  dividend  of  $9.00 
per  share?    $9.00  is  5%  of  what  value? 

7.  If  the  common  stock  of  a  great  steel  manufacturing 
corporation  is  sold  at  72%  (par  value  $100  per  share),  what 
will  be  the  cost  of  300  shares,  including  brokerage  at  f  %? 

8.  If  the  preferred  stock  (par  value  $100  per  share)  of  a 
certain  coal  mining  corporation  sells  at  115%,  what  will  be 
the  cost  of  10  shares  of  it,  including  the  brokerage  of  ^%? 

9.  What  profit  is  made  by  purchasing  100  shares  ($100 
each)  of  stock  of  a  certain  railway  at  97%  and  selling  them  at 
107%,  paying  f  %  brokerage  for  each  transaction? 

10.  How  much  stock  of  a  certain  street  car  company,  incor- 
porated, must  be  purchased  to  insure  an  income  of  $600  from 
it  if  the  stock  pays  semi-annual  dividends  of  4%? 


STOCKS  AND  BONDS— BONDS 


221 


Bonds 

While  corporate  companies  usually  provide  the  necessary 
capital  for  the  conduct  of  their  business, .  through  the  sale  of 
stock  certificates,  they  may  also  provide  for  additional  capital 
by  the  sale  of  bonds,  which  are  generally  secured  by  the  tangible 
property  of  the  corporation,  and  the  bonds  become  the  first 
*<vlien  on  the  business. 

*  In  case  of  default  in  the  payment  when  due,  either  of  the 
accrued  interest  or  of  the  principal,  the  holders  of  the  bonds 
are  in  most  instances  legally  empowered  to  sell  the  property 
of  the  corporation  issuing  the  bonds,  and  to  re-imburse  them- 
selves from  the  proceeds. 

Bonds  bear  a  fixed  rate  of  interest,  while  the  stock  proceeds 
are  governed  by  the  earning  power  of  the  business. 

Bonds  issued  by  the  Federal  government,  by  a  state  or 
by  a  county  must  be  previously  authorized  by  legislation,  or 
by  a  direct  vote  of  the  people,  who  become  the  guarantors. 

On  page  222  is  given  an  illustration  of  a  typical  city 
bond. 

In  addition  to  the  signature  of  the  proper  executive  ofiicers, 
all  stocks  and  bonds  must  have  affixed  to  them  the  seal  of  the 
government,  the  state,  the  county  or  the  business  corporation 
issuing  them. 


Facsimile  of  the  Seal  of 
the  State  of  New  York, 
reduced  to  about  %  of  the 
usable  size. 


Facsimile  of  the  great  Seal 
of  the  United  States,  re- 
duced to  about  }4  of  the 
usable  size. 


Facsimile  of  the  Seal  used 
by  a  business  corporation, 
reduced  to  about  ^  of  the 
usable  size. 


EIGHTH  YEAR 


4 


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STOCKS  AND  BONDS— BONDS 


223 


Detachable  interest  coupons,  or  small  dated  certificates, 
are  generally  issued  with  and  as  a  part  of  each  bond.  These 
are  to  be  separated  from  the  bonds  and  presented  for  payment 
on  the  dates  named  upon  them,^ 


Bonds,  like  stock  certificates,  necessarily  vary  more  or  less  in  statement. 

The  illustration  on  the  preceding  page  shows  the  general  form  of 

a  corporation  bond,  and  the  illustrations  on  this  page 

the  general  form  of  the  detachable  coupons. 

These  coupons  are  usually  transferable,  being  deemed 
equivalent  to  cash,  and  are  collectible  by  any  person  holding 
them. 

Bonds  without  coupons  are  called  registered  bonds,  and 
their  transfer  from  one  holder  to  another  must  be  recorded 
upon  the  books  of  the  corporation  issuing  them. 

What  are  the  advantages  of  registered  bonds  in  case  of  theft? 


Exercise  11 

1.  A  village  issues  corporation  bonds  to  the  amount  of 
$40,000  to  build  a  school  house.  The  bonds  bear  5^%  interest. 
What  is  the  amiount  of  interest  paid  to  the  bondholders  in  one 
year? 

2.  If  a  man  receives  $480  for  the  coupons  of  his  bonds, 

bearing  6%,  what  amount  of  the  bonds  does  he  hold? 

*The  coupons  attached  to  a  bond  are  numbered  from  right  to  left,  or  from 
the  bottom  up.  In  this  way  they  may  be  detached  in  the  order  of  number 
and  date.  For  the  bond  here  illustrated  thirty-nine  coupons  are  required — 
one  for  each  semi-annual  interest  payment  from  January,  1915,  to  January, 
1934 — covering  a  period  of  20  years. 


224  EIGHTH  YEAR 

3.  In  order  to  secure  an  income  of  $1200  annually,  how 
many  bonds  of  the  denomination  of  $100,  bearmg  6%  interest, 
must  I  buy? 

4.  A  bank  buys  50  U.  S.  bonds  of  the  denomination  of 
$1000,  paying  for  them  a  premium  of  3^%  and  a  brokerage 
fee  of  J%.    What  do  the  bonds  cost  the  bank? 

6.  How  much  must  be  paid  for  the  Gas  and  Electric  Com- 
pany bonds  of  a  certain  city,  at  a  premium  of  3%,  the  brokerage 
being  K%? 

6.  If  I  paid  $3200  for  bonds  of  the  face  value  of  $4000 
and  receive  5%  interest  on  the  face  of  the  bonds,  what  do  I 
receive  in  a  year,  and  what  per  cent  do  I  receive  on  my  invest- 
ment? 

7.  Which  is  the  better  investment,  a  5%  bond  bought 
at  $92  for  $100  face  value,  or  a  6%  bond  bought  at  par? 

Suggestion:    $5  is  what  per  cent  of  $92? 

8.  What  must  be  paid  for  5%  bonds  in  order  to  receive 
an  income  of  6%  on  my  investment? 

Suggestion:    $5  is  6%  of  what  amount? 

9.  An  American  business  corporation  operating  a  rubber 
plantation  in  Mexico  issues  bonds  for  $60,000,  payable  in 
15  years.  If  they  are  sold  at  $93  for  $100  of  par  value,  what  is 
realized  from  them  when  80%  of  the  issue  is  "taken,"  or  sold? 

10.  Find  out  what  bonds  have  been  issued  in  your  commu- 
nity. For  what  amounts  were  they  issued?  What  rates  of 
interest  do  they  bear? 

11.  If  a  commercial  corporation  issues  bonds  to  the  amount 
of  $60,000  to  run  eight  years  at  7%,  and  after  paying  interest 
for  five  years  fails,  and  after  a  year  of  delay  pays  only  78% 
of  the  face  of  the  bonds,  what  does  the  holder  of  each  $100  bond 
receive  in  all? 


INVESTMENTS  225 

12.  What  would  he  have  received  on  a  6%  bond  for  the  full 
period? 

13.  To  secure  an  income  of  8%,  how  much  below  par  must 
I  buy  bonds  bearing  6%? 

The  organization  of  an  imaginary  corporation  or  a  study  of 
some  local  corporation  by  the  class  would  prove  an  excellent 
means  of  understanding  stocks  and  bonds.  If  the  time  permits, 
^he  class  should  undertake  such  a  problem. 

INVESTMENTS 

The  supply  or  amount  of  money  on  hand,  together  with  the 
demand  for  loans,  determines,  to  a  large  extent,  the  rate  of 
interest  which  must  be  paid  to  secure  a  loan. 

If  the  supply  of  ready  money  is  large  and  the  demand  for 
loans  is  weak,  the  rate  of  interest  will  be  low. 

On  the  other  hand,  if  the  supply  of  ready  money  is  small 
and  there  is  a  large  demand  for  loans,  the  rate  of  interest  will 
be  high. 

The  risk  involved  in  a  loan  is  also  an  important  factor  in 
determining  differences  in  the  rates  of  loans.  If  the  risk  of 
loss  is  great,  a  high  rate  must  be  paid  to  secure  a  loan.  If  there 
is  very  slight  chance  of  any  loss,  the  rate  of  interest  is  low. 

Many  new  enterprises  are  started  in  the  United  States  every 
year.  Some  of  these  enterprises  are  successful  and  yield  large 
dividends.  On  the  other  hand,  a  large  per  cent  of  these  enter- 
prises fail  and  the  investors  suffer  either  a  partial  or  a  total  loss. 

One  should  never  take  only  the  agent's  word  as  to  the  safety 
of  an  investment,  but  should  consult  some  reliable  disinterested 
party  who  is  well  posted  in  the  field  of  investments,  such  as  a 
reliable  banker  or  broker. 

The  policy  of  "Safety  First"  is  a  very  good  one  to  follow 
in  the  field  of  investments. 


226  EIGHTH  YEAR 

Exercise  12 

1.  Before  the  World  War,  government  bonds  sold  at  pai 
value  when  the  rate  of  interest  was  as  low  as  2%.  The  rates 
of  interest  on  Liberty  Bonds  varied  from  3^%  to  4f  %,  Find 
out  whether  these  bonds  are  now  selling  above  or  below  par. 

2.  Municipal  bonds  usually  bear  from  4%  to  5h%  interest. 
Why  is  the  rate  higher  on  these  bonds  than  on  U.  S.  Govern- 
ment bonds? 

3.  What  is  the  usual  rate  that  is  paid  on  certificates  of 
deposit  or  safety  deposits  in  a  bank? 

4.  Why  are  careful  investments  in  real  estate  considered 
good  investments?  What  are  some  disadvantages  of  such 
investments? 

6.  A  certain  company  advertised  that  they  would  give 
2  shares  of  common  stock  free  with  each  share  of  preferred 
stock  purchased  before  a  certain  date  and  claimed  that  both 
kinds  of  stock  should  soon  be  worth  more  than  par.  Would 
you  invest  in  this  stock?    Why? 

6.  Another  company  advertises  a  certain  sugar  stock  that 
will  pay  10%  on  the  investment.  How  would  the  risk  on  this 
investment  compare  with  a  good  municipal  bond  yielding 
5%  interest? 

7.  The  following  advertisement  appeared  in  a  daily  paper: 
"Absolutely  safe,  exceptionally  profitable,  long-time  invest- 
ment;^ as  good  security  as  municipal  bonds,  with  five  times  the 
returns."  As  an  investor,  how  would  that  advertisement  appeal 
to  you? 

8.  An  agent  for  a  certain  mining  company  was  selling  stock 

at  about  j  of  the  par  value.    He  stated  to  a  prospective  buyer 

that  he  would  guarantee  that  the  value  of  the  stock  would 

'Teachers  should  show  that  the  investment  could  not  yield  five  times 
the  returns  if  the  security  was  as  good  as  municipal  bonds. 


INVESTMENTS  227 

double  in  less  than  6  months.    Would  you  have  bought  this 
stock  on  the  strength  of  the  agent's  statement? 

9.  An  insurance  company  loaned  a  farmer  $3000,  taking 
a  first  mortgage^  on  his  farm  valued  at  $5800.  Was  this  a  safe 
investment  for  the  insurance  company? 

10.  If  you  had  $20,000  to  invest,  would  you  invest  it  in  one 
place  or  divide  it  among  several  forms  of  investment?  Discuss 
the  advantages  and  disadvantages  of  both  of  these  methods. 

Exercise  13 

1.  A  girl  deposited  $75  in  a  State  bank,  receiving  a  certifi- 
cate of  deposit,  bearing  3%  interest.  How  much  interest 
should  she  receive  at  the  end  of  6  months? 

2.  How  much  interest  would  she  have  received  in  a  Postal 
Savings  bank  for  6  months  at  2%?  Was  her  risk  of  losing  her 
money  any  greater  in  the  State  bank  than  it  would  have  been 
in  the  postal  savings  bank? 

3.  If  I  buy  a  municipal  bond  bearing  4^%  interest  for 
$106.50,  including  brokerage,  what  is  the  rate  of  income  on 
my  investment? 

Suggestion:    $4.50  is  what  %  of  $106.50? 

4.  What  is  the  rate  of  income  on  stock  costing  $138.50, 
including  brokerage,  if  the  yearly  dividend  amounts  to  $6.50 
per  share? 

6.  In  deciding  which  is  the  better  investment,  a  municipal 
bond  bearing  4§%  interest,  quoted  at  106f ,  or  a  stock  quoted 
at  138 1  and  known  at  that  time  to  be  yielding  yearly  dividends 
of  $6.50  per  share,  what  other  factors  must  be  considered 
besides  the  present  rate  of  income? 

'A  mortgage  is  a  contract  by  which  the  owner  of  the  property  agrees 
to  let  the  party  loaning  the  money  sell  his  property  to  secure  payment 
for  a  loan  if  he  fails  to  meet  the  terms  stated  in  the  contract. 


228  EIGHTH  YEAR 

6.  A  man  wishes  to  buy  a  city  residence.  It  rents  for  $60 
per  month,  and  he  estimates  that  his  expenses  for  this  property 
would  amount  to  $240  a  year.  How  much  can  he  offer  for  the 
property  if  he  wishes  to  secure  an  income  of  6%  on  his  invest- 
ment? 

7.  A  carpenter  in  a  certain  village  bought  a  house  for  $1875. 
After  spending  $400  on  improvements,  he  sold  the  property 
for  $2850.    Find  his  per  cent  of  gain  on  the  money  invested. 

8.  An  80-acre  farm  sold  for  $4000  in  1900.  In  1903  the 
same  farm  was  sold  for  $4800.  In  1915  it  was  sold  for  $9000. 
Find  the  per  cent  of  increase  in  its  value  between  1900  and 
1903 ;  between  1903  and  1915.  What  other  returns  were  secured 
by  the  owners  beside  the  increase  in  the  value  of  the  land? 

9.  Mr.  Bentley  inherited  $5000  from  his  father.  He  has 
an  opportunity  to  loan  it  to  a  farmer  at  5%  on  a  first  mortgage 
on  a  farm  valued  at  $12,000  or  invest  it  in  a  pecan  grove  which 
an  agent  assures  him  will  yield  10%.  His  banker  tells  him  the 
latter  investment  is  very  risky.    Which  should  he  take? 

10.  An  agent  of  a  mining  company  canvassed  the  citizens 
of  a  small  villS,ge  to  sell  mining  stock.  He  told  them  that  the 
company  wanted  to  keep  the  stock  from  getting  into  the  hands 
of  rich  capitalists.  Would  this  statement  have  induced  you  to 
buy  or  deterred  you  from  investing  in  the  stock? 

11.  A  company  invests  $12,000  in  "stump  lands,"  from  which 
the  pine  timber  has  been  removed,  and  $3000  in  machinery 
to  uproot  and  pulverize  the  stumps,  for  the  extraction  of 
turpentine.  The  annual  profit  is  15%  on  the  investment,  for 
four  years,  at  the  end  of  which  time  the  land  has  doubled  in 
value,  and  the  machinery  is  sold  for  half  the  cost  price.  What 
is  the  real  per  cent  of  annual  profit? 

12.  Does  it  pay  to  invest  money  in  an  education?  See  if  you 
can  get  figures  to  prove  your  answer  to  that  question? 


/  BANKS  AND  BANKING.    REVIEW  229 

Exercise  14 

1.  State  5  services  that  banks  perform  for  us. 

2.  Tell  how  to  open  an  account  at  a  bank. 

3.  How  can  you  withdraw  money  which  you  have  on  deposit 
at  a  bank? 

4.  What  special  precautions  should  be  taken  in  filling  out  a 
check? 

5.  Show  two  ways  in  which  a  check  may  be  indorsed.     What 
are  these  kinds  of  indorsement  called? 

6.  What  should  you  do  in  the  event  that  you  lose  a  check 
made  out  to  you? 

7.  What  are  the  advantages  of  paying  bills  by  checks? 

8.  What  are  the  interest  rules  in  your  local  savings  banks? 
How  do  they  differ  from  those  given  on  page  204? 

9.  What  is  bank  discount? 

10.  Find  the  bank  discount  for  90  days  on  a  note  for  $350  for 
1  year,  bearing  7%  interest.     The  discount  rate  is  6%. 

11.  What  is  a  draft?    Name  and  describe  two  kinds  of  drafts. 

12.  What  is  a  clearing  house  for  the  banking  system? 

13.  Find  the  cost  of  a  draft  for  $2000  when  money  is  at  a 
premium  of  |^%. 

14.  Tell  how  a  bank  is  organized. 

15.  Give  an  account  of  the  origin  of  the  term,  bankrupt. 

16.  What  is  the  minimum  amount  of  capital  stock  that  is 
necessary  for  the  organization  of  a  national  bank? 

17.  What  was  the  purpose  of  the  organization  of  our  Federal 
Reserve  banks? 

18.  What  is  the  minimum  amount  of  capital  stock  that  is 
required  for  a  Federal  Reserve  bank? 

19.  Why  are  national  bank  notes  as  good  as  government 
"greenbacks"? 


230  EIGHTH  YEAR 

Exercise  16 

1.  What  is  a  corporation? 

2.  What  is  the  usual  par  value  of  the  shares  of  a  corporation? 

3.  Why  do  most  men  prefer  to  organize  as  a  corporation 
than  as  a  partnership? 

4.  What  is  a  dividend?    What  is  brokerage? 

6.  What  is  the  difference  between  common  and  preferred 
stock? 

6.  Find'  the  cost  of  50  shares  of  stock  bought  at  104j, 
brokerage  |%. 

7.  Find  the  amount  of  the  proceeds  which  the  owner  of  the 
50  shares  of  stock  (mentioned  in  the  preceding  problem)  would 
receive,  brokerage  ^%. 

8.  What  is  the  difference  between  the  stock  certificates  and 
the  bonds  of  a  corporation? 

9.  What  is  a  coupon  bond?  A  registered  bond?  Which  is 
the  easiest  to  transfer  to  another  party?  Which  is  safest  from 
danger  of  theft? 

10.  What  are  the  chief  factors  which  determine  the  rate  of 
interest  which  must  be  paid  to  secure  a  loan? 

11.  What  are  the  safest  forms  of  investment? 

12.  An  owner  of  a  cottage  offered  it  for  29  one-hundred  dollar 
bonds  which  were  then  selling  at  91.  What  was  the  value 
which  he  placed  on  his  cottage,  making  no  allowance  for  bro- 
kerage? 

13.  What  is  a  mortgage? 

14.  A  firm  with  a  capital  stock  of  $20,000,000  declared  an 
annual  dividend  of  8%  on  its  stock.  What  was  the  total 
amount  of  the  dividends?  How  much  would  a  man  receive 
who  owned  75  shares  of  this  stock? 

16.  Find  the  cost  of  five  Liberty  3^%  Bonds  at  their  quota- 
tion in  today's  paper,  brokerage  |%. 


CHAPTER  III 

REMITTING  MONEY 

On  account  of  the  heavy  expense  of  shipping  actual  money, 
much  of  the  business  of  the  country  is  carried  on  by  means  of 
commercial  forms  of  various  kinds. 


Postal  Money  Order 

One  of  the  most  common  forms  for  sending  small  amounts  of 
money  is  the  postal  money  order.  The  government  charges  a 
small  fee  for  these  orders,  varying  with  the  amount  of  the  order. 


m.°L        "-OS  Angeies,  CaL  193989 

United  States  Postal  Money  Order 


envn  wHti'ykC-SIVUX.  OF  HO  VAUJr* , 


f  81 100"  *""""• '^"'    193989 

i  •''^^^"■•"     Cotfpon  for  Paying:  Office 

" >^ BOU-AM    '     .  I.    f- 


T10N  on  CRASURC  RCNDCKS  r 


The  following 

Not  exceeding 

Exceeding  $  2 

Exceeding      5 

Exceeding 

Exceeding 

Exceeding 

Exceeding 

Exceeding 

Exceeding 

Exceeding 


table  shows  the  fees  for  the  various  amounts: 

$2.50 3^ 

.50  and  not  exceeding    $  5.00 5^ 

.00  and  not  exceeding      10.00 S^ 

.00  and  not  exceeding      20.00 10^ 

.00  and  not  exceeding     30.00 12^ 

00  and  not  exceeding     40.00 15^ 

,00  and  not  exceeding      50.00 18ji 

00  and  not  exceeding     60.00 20^ 

00  and  not  exceeding      75.00 25fi 

.00  and  not  exceeding    100.00 30^ 


231 


232 


EIGHTH  YEAR 


Actual  money  may  be  sent  by  registered  mail  for  a  charge 
of  10  cents  in  addition  to  the  regular  postage.  An  indemnity 
not  to  exceed  $25.00  will  be  paid  by  the  government  if  a  first- 
class  package  or  letter  is  lost. 

Exercise  1 

1.  How  much  will  money  orders  for  the  following  sums 
cost:    $2.50;  $15.00;  $30.00;  $52.14;  $7.25;  $75.00? 

2.  Which  will  be  cheaper,  to  send  $25  in  a  letter  by  regis- 
tered mail  or  to  buy  a  postal  money  order  for  $25?  (The 
postage  on  the  letter  is  extra  in  both  cases.) 

3.  Which  is  cheaper,  sending  $10  by  registered  mail  or 
sending  a  postal  money  order  for  $10? 

4.  What  is  the  fee  on  a  postal  money  order  for  $5.00; 
for  $50.00;  for  $100.00? 

Express  Money  Orders 

Express  companies  issue  express  money  orders  which  are 
similar  in  form  to  the  postal  money  order  and  for  which  the 
same  fees  are  charged.  The  table  on  page  231  may  also  be  used 
in  computing  charges  on  express  money  orders. 


H 


I  Wmkn  Countcksighcd      .  ■»-.:i--»-^^.— .U'1.I=I.IJA 


15*0000000 


SAMPLE- 
NOTOOOO, 


JtHaBo'^^. 


=/irD0UAK8 


^^rrfr- 


%^ ^y^  evlt*t.A.^i^ 


15-0000000 


•ouTTur*  Mcurr 


1^^ 


I  &£•- 


An  Express  Money  Order 


REMITTING  MONEY— DRAFTS 


233 


Exercise  2 

1.  Who  purchased  the  express  money  order  here  shown? 

2.  To  whom  is  this  order  made  payable? 

3.  How  could  Mr.  Brooks  transfer  this  order  to  some  other 
person  for  collection? 

4.  How  much  will  an  express  money  order  for  $18.75  cost? 
6.  How  much  will  an  express  money  order  for  $50  cost? 


X 


Bank  Drafts 

A  bank  draft  is  really  a  check  by  one  bank  on  another  bank. 
For  regular  patrons  of  the  bank  who  have  checking  accounts, 
most  banks  write  drafts  for  small  amounts  without  extra 
charge  as  a  matter  of  accommodation.  For  large  amounts 
drafts  are  sold  at  a  'premium  or  a  discount,  depending  on  the 
state  of  the  balance  between  the  banks  of  the  two  cities  involved. 


fii    II      II I 


A  Bank  Draft 


Exercise  3 

1.  Where  was  the  above  draft  purchased? 

2.  To  whom  was  it  made  payable? 

8.  How  can  it  be  transferred  to  some  other  person? 


234  EIGHTH  YEAR 

4.  On  what  bank  is  the  draft  drawn? 

6.  A  farmer  wishes  to  pay  off  the  mortgage  on  his  farm 
that  is  held  by  a  certain  insurance  company.  He  finds  that 
the  rate  for  a  draft  on  the  city  where  the  insurance  company 
is  located  is  20  cents  per  $100.  Find  the  cost  of  the  draft  for 
$3000. 

6.  How  much  would  an  express  money  order  for  the  same 
amount  have  cost  him? 

Checks 

Business  firms  and  most  individuals  have  checking  accounts 
in  some  bank.  Instead  of  buying  drafts,  most  firms  send 
checks  to  settle  their  accounts.  A  check  is  returned  by  the 
local  bank  to  the  firm  who  issues  it  when  the  account  is  bal- 
anced.  The  check  thus  serves  as  a  receipt  for  the  transaction. 


5-39 


Orper  n^  J^y^'^VW'^X  .^^^^^y,^;^^  (^  <p^^O\ 


^^^.^n/7-L^^^^^.n)^:^  ^  /^ 


A  Business  Firm's  Check 

Exercise  4 

1.  What  firm  issued  the  above  check?    In  what  bank  do 
they  carry  their  banking  account? 

2.  To  whom  is  this  check  made  payable? 

3.  When  the  check  is  returned  to  the  First  National  Bank 
of  Boston  for  collection,  how  will  they  enter  it  on  their  accounts? 


REMITTING  MONEY— CHECKS  235 


W^^K^/Tl.^  ^{,^^/V     .yW  /^^^ 


TlRST]SATIO:KMrBA]VKOr  CfflCAGOii  1 


PAY  TO  THE  ORDER  OF 


cT  973647  J^^^^..,^^ 


A  Personal  Check 

4.  Who  issued  the  above  personal  check?  To  whom  is  it 
made  payable?  Show  how  this  check  would  have  to  be  indorsed 
when  it  is  cashed.     (See  page  202.) 

6.  If  a  certain  man  has  a  balance  of  $125.82  in  the  bank 
on  Jan.  1,  1917,  and  issues  three  checks  as  follows:  for  rent, 
$35.00;  for  Ught  bill,  $1.58;  for  gas  bill,  $2.56;  how  much  will 
he  have  to  his  credit  in  the  bank? 

6.  Mr.  Hill  issues  Mr.  Johnson  a  check  for  $25.00  to  pay 
for  services  rendered.  Mr.  Johnson  loses  the  check  and 
promptly  notifies  Mr.  Hill  of  his  loss.  How  can  Mr.  Hill 
arrange  to  pay  Mr.  Johnson  without  danger  of  having  to  pay 
twice  should  the  check  be  found  at  a  later  date? 

7.  Why  do  banks  refuse  to  cash  checks  for  strangers? 

8.  Discuss  the  advantages  and  disadvantages  of  remitting 
money  by  means  of  checks. 

Foreign  Remittances 

Remittances  to  foreign  countries  may  be  made  by  inter- 
national money  orders,  by  foreign  express  orders  or  by  foreign 
drafts  called  6t7Zs  o/  exchange. 


236  EIGHTH  YEAR 

Emergency  Remittances 
When  an  agent  wishes  money  immediately  in  order  to  close 
an  important  transaction,  he  often  finds  it  an  advantage  to 
have  his  firm  telegraph  him  the  money. 

In  the  telegram  in  the  illus- 

THE  WESTERN  UNION  TELEGRAPH  COMPANY*        tration  Richard  Doe  of  Wash- 

_      I — i?!!!!!I'^~T*" ''°**"  _  ■- — ==        ington  is  sending  his   brother 

■ — —  ;^A^^..!I^^<f4^T-«-  John   Doe  in   New  Orleans  a 

Traganf  yj.     ^  Certain  sum  of  money  by  tele- 

ff  /I ,    a  ^y  j^  ^/y,    jr„,  graph.      In   order   to    prevent 

^/^..^rrW^y.^/i^^J^o^  ^^l.rgLJ^y^f^^      othcrs  from  learmng  about  the 

ritiif  (M/fM-^nu-  ,^4e/a/iJrTu  c/'aii. amouut  of  mouey  involved  in 

>iLT\o  ixd-^y  Hprii^--  the  transaction,  the  message  is 

expressed  in  terms  of  a  code. 

MCnHM  TKtS  MDUOC  TO  m*Mmi  AOEMT  M  lOOII  M  HUT 

The  word  ring  in  the  telegram 
refers  to  the  amount  of  money  and  can  be  understood  only  by  a  person 
familiar  with  that  particular  code. 

Note  the  writing  in  the  last  line.  It  was  made  by  the  sending  agent 
with  his  left  hand  while  he  was  transmitting  the  message  with  his  right 
hand,  showing  a  high  degree  of  eflficiency  in  operation. 

Upon  the  receipt  of  this  message,  the  agent  in  New  Orleans  sends  to 
John  Doe  the  following  notice: 

"We  have  received  a  telegraphic  order  to  pay  you  a  sum 
of  money  upon  satisfactory  evidence  of  identity.  The  amount 
win  be  paid  at  our  office  if  called  for  within  72  hours;  other- 
wise under  our  arrangement  with  the  remitter  the  order  will 
be  canceled  and  the  amount  thereof  refimded." 

When  money  is  remitted  by  telegraph,  there  is  a  transfer  charge 
on  the  money  in  addition  to  the  regular  charge  for  the  telegram 
which  is  computed  on  the  basis  of  a  15-word  message. 

Exercise  5 

1.  In  remitting  $25  (or  less)  by  telegraph  between  certain 
cities,  the  charge  for  that  amount  is  60  cents.  The  telegraph 
charges  between  these  cities  is  35  cents  for  a  15- word  message. 
Find  the  transfer  charge  for  that  amount. 


REMITTING  MONEY— BY  CABLE  237 

2.  What  would  be  the  cost  of  remitting  $25  by  an  express 
money  order?  How  much  cheaper  is  the  express  money  order 
than  the  remittance  by  telegraph  given  in  Problem  1?  When  is 
money  usually  remitted  by  telegraph? 

3.  The  cost  of  a  15-word  message  between  two  cities  is 
35  cents.  What  will  be  the  total  charges  for  remitting  $100  by 
telegraph  if  the  transfer  charges  for  the  money  are  85  cents 
per  $100? 

4.  The  charges  for  remitting  $200  by  telegraph  between 
those  cities  are  $1.45.  How  much  is  charged  for  the  extra 
$100?  At  the  same  rate  per  $100  beyond  the  first  $100,  what 
will  be  the  charges  on  remitting  $1000  between  those  cities? 

Remitting  by  Cable 

If  an  emergency  arises  for  a  quick  transmission  of  money 
to  a  firm  or  person  in  a  foreign  country,  money  can  be  remitted 
by  cable  in  the  same  manner  that  it  is  telegraphed  in  this 
country.  The  amount  of  the  money  is  then  expressed  in  the 
money  values  of  the  foreign  country  to  which  it  is  sent.  The 
following  illustration  shows  a  form  for  such  a  cablegram: 

In  the  cablegram  shown  in  f^^sSSSSSSSSS^SSS^^^^^^^^M 

the  illustration  "Bruzzolo,  Lon-  HISP^^^^I^SEBSQSE^D^^^HB 

don"  stands  for  the  registered  W^^^JSSmSaS^itmmB^m 

address  of  the  London  telegraph  j^^^^^^^i^^^^^^^' 

office    that    pays    the    money.  ' '"     ^        ';S^  %^,"^P"a?'5"';/V 

"Rabbit"  is  a  guard  word  neces-  ^^.^^zivyy^^^^^ 

sary  in  sending  such  messages.  ^            _(^ — • 

"Jewel"  is  the  code  word  for  — ^^^>=*t"^  f^  ■:^-- 

"pay    tx,."      "John    Doe,    76  Z^^^^'^T^'^t^^^ 

Downing  Street,  London"  is  the .-^crtZa.rCtL.^^ 

payee.     "Bracket"   is   a  code  ^ 

word    which    stands    for    the     1  J!^:T"t:^"'^-^''^.z':tth::z~"^^ — 'iifirr'" 
amount  to  be  paid  John  Doe.  "" 

"Darby"  means  "from."  "Richard  Roe"  is  the  name  of  the  sender  of  the 
money  and  "Jentant"  is  the  code  word  standing  for  the  signature  of  the 
transfer  agent  at  New  York. 


238  EIGHTH  YEAR 

Exercise  6 

The  charges  on  sending  money  by  cablegram  are  $4.65  for 
the  cable  charges  (15  words)  and  1%  premium  on  the  amount 
of  money  sent. 

1.  Find  the  total  amount  that  must  be  paid  the  agent  in 
New  York  to  remit  $100  to  a  party  in  London. 

2.  What  will  be  the  transfer  charges  on  remitting  $500 
by  cable?  Find  the  total  amount  which  must  be  paid  the 
transfer  agent  in  this  country. 

8.  If  the  word  "Bracket"  stands  for  $250,  how  much  did 
Richard  Roe  have  to  pay  the  transfer  agent  in  New  York? 

4.  Find  the  total  transfer  charges  by  cable  on  $300,  on 
$1000,  on  $5000. 

Remitting  Money  by  Wireless 

To  facilitate  business,  leading  banks  and  express  companies, 
in  normal  times,  keep  large  amounts  of  money  on  deposit  at 
the  principal  commercial  centers  in  the 
European  countries.  During  the  period  of 
the  European  War  communication  with 
certain  countries  in  Europe  was  maintained 
mostly  by  radio  means,  and  the  transmission 
of  money  by  "wireless"  reached  large  pro- 


MONEY  REMITTED  BY 

WIRELESS 

Gtmaiiy  and  Austria-Huitgary 

Takrk***  lUadalpk  4301 

Fort    Dearborn 
National    Bank 


portions  at  rates  indicated  in  the  following  problem: 

Exercise  7 
1.  A  firm  in  Chicago  remitted  $1000  by  a  wireless  radiogram 
to  a  firm  in  Berlin  on  Jan.  28,  1917.  The  charges  were  quoted 
by  the  bank  at  $4.00  per  order  of  6  words,  plus  the  usual  postal 
charges  of  15  cents  per  order,  excess  words  to  be  paid  at  the 
rate  of  57  cents  per  word.  If  the  radiogram  contained  9  words, 
what  were  the  charges  on  the  radiogram? 


CHAPTER  IV 

PRACTICAL  MEASUREMENTS 

Exercise  1.    Review  of  Quadrilaterals 

1.  State  the  principle  for  finding  the  area  of  a  rectangle. 

2.  What  is  the  area  of  a  rectangle  16  inches  long  and  8f 
inches  wide?     (See  page  151.) 

3.  Find  the  number  of  square  yards  in  the  area  of  a  baseball 
diamond  which  is  90  feet  square. 

4.  How  many  square  inches  are  there  in  a  sheet  of  paper 
8^  inches  by  11  inches?  How  many  square  feet  of  space  would 
a  ream  of  500  sheets  of  this  paper  cover  if  the  sheets  were 
placed  edge  to  edge? 

6.  How  many  square  feet  are  there  in  a  rectangular  garden 
15  yards  long  and  30  feet  wide?    How  many  square  yards? 

6.  A  certain  farm  is  1  §  miles  long  and  f  of  a  mile  wide. , 
How  many  square  rods  does  it  contain?    How  many  acres? 

7.  A  field  60  rods  long  and  40  rods  wide  yielded  360  bushels 
of  wheat.    What  was  the  yield  per  acre? 

8.  There  are  usually  40  apple  trees  planted  on  an  acre  of 
ground.  How  many  square  feet  of  space  does  that  allow  for 
each  tree? 

9.  A  ball  club  bought  a  field  for  a  ball  park.  It  was  400 
feet  long  and  395  feet  wide.  How  much  did  it  cost  at  $310 
an  acre? 

10.  School  architects  usually  allow  16  square  feet  of  space 
as  the  proper  amount  for  each  pupil.  How  many  pupils  can 
be  properly  seated  in  a  school  room  24'  x  28'? 

239 


240  EIGHTH  YEAR 

11.  How  many  pupils  are  there  in  your  school  room?  Find 
the  number  of  square  feet  of  floor  space  for  each  pupil,  using 
the  total  area  of  the  room  for  the  computation. 

12.  The  area  of  a  rectangle  is  96  square  inches  and  the  base 
is  16  inches.    Find  the  altitude.* 

13.  The  area  of  a  rectangle  is  -yo  of  a  square  foot.  The 
width  is  ^  of  a  foot.    What  is  the  length? 

14.  Find  the  area  of  a  parallelogram  with  a  base  of  18  inches 
and  an  altitude  of  12  inches.     (See  page  156.) 

15.  The  length  of  a  parallelogram  is  f  of  a  foot  and  the  alti- 
tude is  f  of  a  foot.    What  is  its  area? 

16.  Find  the  area  of  a  trapezoid  with  its  parallel  sides 
equal  to  8  inches  and  15  inches  and  its  altitude  equal  to  12 
inches.     (See  page  158.) 

17.  Two  converging  roads  form  a  field  in  the  shape  of  a 
trapezoid.  The  two  parallel  sides  are  60  rods  and  100  rods 
and  the  altitude  is  64  rods.  How  many  acres  are  there  in  this 
field? 

18.  How  much  is  this  tract  of  land  worth  at  $175  an  acre? 

Exercise  2.    Review  of  Triangles 

1.  State  the  principle  for  finding  the  area  of  any  triangle. 

2.  What  is  the  area  of  a  triangle  whose  base  is  8  inches  and 
whose  altitude  is  7  inches?     (See  page  160.) 

3.  The  area  of  a  triangle  is  54  square  inches  and  the  altitude 
is  9  inches.    Find  the  base. 

4.  The  area  of  a  triangle  is  J  of  a  square  foot  and  the  base 
is  f  of  a  foot.    Find  the  altitude. 

6,  A  triangular  flower  bed  has  a  base  of  3  yards  and  an 
altit'Jde  of  4  yards.    Find  its  area  in  square  yards. 


PRACTICAL  MEASUREMENTS— SQUARES      241, 

Squares  and  Square  Roots 
A  square  is  a  rectangle  with  all  of  its  sides  equal. 
What  kind  of  angles  has  a  square? 
If  a  side  of  a  square  is  4,  the  base  and  altitude  are 


each  4,  and  the  area  of  the  square  is  4X4,  or  16.  ^  Square 

16  is  called  the  square  of  4.    This  may  be  written  4^  =  16. 

The  small  figure  2  at  the  upper  right  hand  side  of  the  four 
is  called  an  exponent.  An  exponent  shows  how  many  times  the 
number  is  taken  as  a  factor.  For  example,  5^  means  that  5 
is  taken  twice  as  a  factor,  or  5X5. 

— ^  /  ? 

Exercise  3  t.  -  >/ 

1.  Make  a  table  showing  the  squares  of  all  numbers  from 

1  to  25  as  follows:  j 

1P  =  ? 
122=? 
132  =  ?     ' 
142=?  ; 
152=? 

2.  Learn  this  table  so  that  you  can  give  any  square  quickly. 

3.  What  are  the  squares  of  30,  40,  50,  60,  70,  80? 

Since  16  is  the  square  of  4,  4  may  be  called  the  square  root 
of  16.  The  two  equal  factors  of  16  are  4  and  4.  One  of  the 
equal  factors  of  a  number  is  called  the  root  of  the  number. 

In  order  to  find  the  square  root  of  a  number,  we  must  find 
a  factor  which,  when  multiplied  by  itself,  will  give  the  number. 

Square  root  is  very  important  in  solving  problems  in  right 
triangles. 

4.  What  are  the  square  roots  of  4,  9,  25,  36,  49,  64,  81,  100, 
144,  225,  625? 


12=     1 

62  =  ? 

22=  4 

72=? 

32=  9 

82=? 

42=16 

92=? 

52=25 

102=? 

162  =  ? 

212  =  ? 

/a 

172=? 

222  =  ? 

5  t 

182  =  ? 

232=? 

192=? 

242=? 

202  =  ?' 

252=? 

'  J 

66 


242  EIGHTH  YEAR 

5.  Find  the  square  root  of  1296. 

The  number  1296  is  larger  than  any  of  the  squares  that  we 
have  learned,  so  it  is  more  difficult  to  see  the  square  root  of 
this  number  than  those  in  Problem  4.  Try  different  numbers 
until  you  find  one  which  multiplied  by  itself  will  give  1296. 

There  is  a  much  more  convenient  method  of  finding  the 
square  root  of  a  number  than  trying  various  numbers  until 
we  find  the  correct  one.  The  following  form  shows  the  method 
of  extracting  the  square  root  of  a  number: 

Extracting  the  Square  Root  of  a  Number 

1.  Begin  at  the  decimal   point  and  point 
1296'    36     ®ff  *^^  number  into  periods   of  two  figures 
9    *  each  (12'960. 

396  2.  Find  the  largest  square  (9)  in  the  left- 

396  hand  period   (12).      Put  its  square  root   (3) 

as  the  first  figure    of  the  square  root  and 
subtract  the  square  (9)  from  the  first  period  (12). 

3.  To  the  remainder  (3)  bring  down  the  next  period  (96). 

4.  Tate  two  times  the  number  in  the  root  (3)  and  use  this 
product  (6)  as  a  partial  divisor  into  the  first  figure  or  two 
figures  of  the  remainder  (396).  Place  the  figure  thus  obtained 
(6)  as  the  next  figure  of  the  square  root.  Also  add  this  figure 
(6)  to  the  partial  divisor,  making  the  complete  divisor  (66). 

5.  Multiply  this  complete  divisor  by  the  last  figure  of  the 
root  (6). 

6.  If  there  are  other  periods  proceed,  as  in  steps  3,  4  and  5. 
There  is  no  remainder  in  this  problem. 

The  square  root,  then,  of  1296  is  36. 

By  reference  to  the  following  diagram  on  cross  section  paper 
the  reasons  for  the  various  steps  in  the  preceding  problem 
can  be  understood : 


-tens  X  unit; 


30  X  e 


S 


of  tens 


m 


=  900 


Units 


PRACTICAL  MEASUREMENTS— SQUARE  ROOT      243 

When  the  number  1296  is  separated  into  two  periods,  the 
period  12  really  stands  for  1200  and  contains  the  square  of  the 
tens  figures  in  the  root. 
The  largest  square  of 
tens  contained  in  1200 
is  900  or  the  square 
of  3  tens  (or  30).  Note 
in  the  diagram  at  the 
right  the  large  square 
of  the  three  tens  (or 
30)  which  contains  900 
of  the  small  squares. 

In  order  to  find  the 
units  figure,  the  900 
must  be  taken  from 
the  1200,  leaving  300 
of    the    small    squares. 

To  these  must  be  added  the  next  period,  96,  making  the 
total  remainder,  396.  This  means  that  396  small  squares 
compose  the  two  rectangles  and  the  small  square  at  the  top 
and  right-hand  side  of  the  figure.  Since  the  two  rectangles 
have  the  same  length  as  the  large  square,  each  rectangle 
is  3  tens  or  30  units  long.  There  are  two  of  the  rectangles 
and  so  both  of  them  are  2X3  tens  or  6  tens  or  60  units  long. 
Using  60  as  a  partial  divisor  into  the  396,  we  can  find  the 
altitude  of  the  rectangles,  which  we  find  to  be  approximately 
6  units. 

Adding  the  lengt.h  of  the  small  square  (approximately  6) 
to  the  length  of  the  two  rectangles,  we  have  a  rectangle  which 
is  approxhnately  66  units  long  and  6  units  wide: 


Mi 


^3o 


nm 


i 


244 


EIGHTH  YEAR 


When  the  base  66  of  this  long  rectangle  is  multiplied  by  the 
altitude  6,  we  find  that  the  two  rectangles  and  the  small  square 
which  formed  this  long  rectangle  were  composed  of  396  small 
squares,  which  made  up  the  remainder  after  the  large  square 
had  been  subtracted  from  the  figure. 

The  square  root  then  consists  of  3  tens  and  6  units,  or  36. 


Exercise  4 

Find  the  square  roots  of  the  following  numbers: 


1. 
2. 
3. 
4. 
6. 
6. 
7. 


256 
1156 
1764 
4489 
3364 
5184 
7056 


8. 

9. 
10. 
11. 
12. 
13. 
14. 


3969 
5041 
11025 
18225 
1225 
6889 
9604 


16. 

3249 

16. 

116964 

17. 

173889 

18. 

822639 

19. 

123904 

20. 

229441 

21. 

42436 

Find  the  square  roots  of  the  following  numbers: 


1. 


3 


27 


'3.00'00'00'|1732-|- 

1 
[200 

189 


343 


1100 
1029 


3462 


7100 
6924 


If  the  square  root  does  not  come  out 
as  an  integer,  add  ciphers  in  periods 
of  two  each  and  proceed  as  in 
other  problems.  For  practical  pur- 
poses it  is  not  necessary  to  carry 
the  result  beyond  3  decimal  places. 


2.  15. 

3.  13. 


4.  34. 
6.  12. 


6.  50. 

7.  18. 


8.  5. 

9.  16. 


10.  83. 

11.  45. 


Compare  your  results  in  these  problems  with  the  values 
found  in  the  following  table: 


PRACTICAL  MEASUREMENTS— SQUARE  ROOT      245 


SQUARE  ROOTS  OF  NUMBERS 

From  1  to  100,  Carried  to  Three  Places  of  Decimals 


Nximber 

Square  Root 

Number 

Square  Root 

Number 

Square  Root 

1 

1 

34 

5.831 

67 

8.185 

2 

1.414 

35 

5.916 

68 

8.246 

3 

r.732 

36 

6 

69 

8.307 

4 

"2 

37 

6.083 

70 

8.367 

5 

2.236 

.38 

6.164 

71 

8.426 

6 

2.449 

39 

6.245 

72 

8.485 

7 

2.646 

40 

6.325 

73 

8.544 

8 

2.828 

41 

6.403 

74 

8.602 

9 

3 

42 

6.481 

75 

8.660 

10 

3.162 

43 

6.557 

76 

8.718 

11 

3.317 

44 

6.633 

77 

8.775 

12 

3.464 

45 

6.708 

78 

8.832 

13 

3.606 

46 

6.782 

79 

8.888 

14 

3.742 

47 

6.856 

80 

8.944 

15 

3.873 

48 

6.928 

81 

9 

16 

4 

49 

7 

82 

9.055 

17 

4.123 

50     - 

7.071 

83 

9.110 

18 

4.243 

51 

7.141 

84 

9.165 

19 

4.359 

52 

7.211 

85 

9.220 

20 

4.472 

53 

7.280 

86 

9.274 

21 

4.583 

54 

7.348 

87 

9.327 

22 

4.690 

55 

7.416 

88 

9.381 

23 

4.796 

56 

7.483 

89 

9.434 

24 

4.899 

57 

7.550 

90 

9.487 

25 

5 

58 

7.616 

91 

9.539 

26 

5.099 

59 

7.681 

92 

9.592 

27 

5.196 

60 

7.746 

93 

9.644 

28 

5.291 

61 

7.810 

94 

9.695 

29 

5.385 

62 

7.874 

95 

9.747 

30 

5.477 

63 

7.937 

96 

9.798 

31 

5.568 

64 

8 

97 

9.849 

32 

5.657 

65 

8.062 

98 

9.899 

33 

5.745 

66 

8.124 

99 
100 

9.950 
10 

You  will  find  it  an  advantage  to  use  the  preceding  table  to  find  the 
square  roots  of  all  numbers  between  1  and  100.  Engineers  and  advanced 
students  of  mathematics  and  science  use  books  with  similar  tables. 


246  EIGHTH  YEAR 

Exercise  6 

1.  The  area  of  a  square  is  64  square  inches.    What  is  the 
length  of  one  side? 

2.  The  area  of  a  square  is  40  square  inches.    What  is  the 
length  of  one  side? 

3.  A  square  field  contains  40  acres.    What  is  the  length 
of  one  side  in  rods? 

4.  What  is  the  length  of  one  side  of  a  square  whose  area 
is  81  square  yards? 

5.  What  is  the  length  of  one  side  of  a  square  whose  area  is 
64  square  yards? 

6.  By  the  use  of  the  table  find  the  square  roots  of  the 
following  numbers:     17,  56,  97,  62,  43,  35,  2,  5,  77,  32. 

Right  Triangles 

A  right  triangle  has  one  right  angle.  The 
other  two  angles  of  a  right  triangle  are 
always  acute. 

In  the  right  triangle  A  B  C,  A  C  and  A  B 
are  called  the  legs  and  B  C  is  called  the 
hypotenuse. 

Suppose  the  side  A  C  is  3  inches  long  and  A  B  is  4  inches 
long,  as  shown  in  the  figure  below: 

Exercise  6 

1.  How  many  square  inches 
are  there  in  the  square  constructed 
on  the  leg  that  is  4  inches  long? 

2.  How  many  square  inches  are 
there  in  the  square  constructed 
on  the  leg  that  is  3  inches  long? 


PRACTICAL  MEASUREMENTS— RIGHT  TRIANGLE  247 

3.  How  many  square  inches  are  there  in  the  square  on  the 
hypotenuse,  which  is  shown  to  be  5  inches  long? 

4.  How  does  the  square  on  the  hypotenuse  compare  in 
size  with  the  number  of  square  inches  in  the  sum  of  the  two 
squares  on  the  legs? 

This  relation  may  then  be  stated  in  the  following  principle: 

PRINCIPLE:    In  a  right  triangle,  the  square  of  the  hypotenuse 
is  equal  to  the  sum  of  the  squares  of  the  other  two  sides.^ 

Exercise  7 

1.  The  two  legs  of  a  right  triangle  are  15  feet  and  20  feet. 
Find  the  hypotenuse. 

Solution:  152  =  225;  20^=400.  The  sum  of  the  squares 
on  the  two  legs  =  225+400  =  625,  which  is  equal  to  the  square 
on  the  hypotenuse. 

The  hypotenuse  then  must  be  the  square  root  of  625  which 
is  25. 

Therefore:    The  hypotenuse  is  25  feet  long. 

2.  The  hypotenuse  of  a  right  triangle  is  20  inches  and  one 
of  the  legs  is  12  inches.    Find  the  length  of  the  other  leg. 

Solution:  Since  the  square  on  the  hypotenuse  (400)  is 
equal  to  the  sum  of  the  squares  on  the  two  legs,  the  square 
on  either  leg  must  be  equal  to  the  difference  between  the 
square  on  the  hypotenuse  and  the  square  on  the  other  leg  (144). 
The  square  of  the  unknown  leg =400— 144  =  256. 

The  leg  is  the  square  root  of  256  =  16.  Therefore :  The  leg  is 
16  inches  long. 

3.  A  right  triangle  has  two  legs  equal  to  6  feet  and  8  feet. 

What  is  the  length  of  the  hypotenuse? 

^This  principle  was  first  stated  by  Pythagoras,  a  Greek  mathematician, 
over  2000  years  ago. 


248 


EIGHTH  YEAR 


These  dimensions  are  very  frequently  used  in  constructing 
a  right  angle  with  cords.  By  making  the  two  sides  6  feet  and 
8  feet  and  then  using  a  10-foot  cord  to  regulate  the  spread 
of  the  two  sides  an  accurate  right  angle  can  be  formed. 

Find  the  missing  leg  or  the  hypotenuse  in  the  following 
problems:  (Carry  to  three  decimal  places  if  the  result  does  not 
come  out  even.) 

Leg  heg                           Hypotenuse 

4.    5  in.  12  in.                                     ? 

6.    8  in.  ?                                   17  in. 

6.  24  ft.  32  ft.                                  •  ? 


7.  ? 

8.  7  in. 

9.  14  rd. 
10.  27  in. 


24  in. 

11  in. 

9 


30  in. 
? 

18  rd. 


36  in.  ? 

11.  What  is  the  length  of  the  diagonal 
of  a  square  that  is  8  inches  on  each  side? 

12.  A  baseball  diamond  is  90  feet 
square.  How  far  is  it  from  first  base  to 
third  base? 

13.  A  congressional  township  is  6 
miles  square.     How  long  would  a  road 

be  if  it  ran  on  the  diagonal  line  of  the  square?  How  much 
shorter  is  this  road  than  one  which  goes  along  the  two  sides 
of  the  square  to  the  opposite  comer? 

14.  Draw  a  square  4  inches  on  each  side. 

Divide  it  into  two  equal  squares. 

Suggestion:  Draw  the  two  diagonals  as  shown 
in  the  illustration.  Cut  along  the  dotted  diagonals, 
thus  dividing  the  square  into  4  parts.  See  if  you 
can  arrange  these  parts  so  that  they  will  make  two 
smaller  squares. 

15.  How  long  is  the  side  of  one  of  the  small  squares? 


PRACTICAL  MEASUREMENTS— PROBLEMS        249 


16.  Two  boys  were  making  a  model  of  an  automobile  in  a 
wood  shop.  They  were  making  out  a  bill 
for  lumber  which  they  wished  to  order. 
The  sides  of  the  hood  were  12  inches 
apart,  and  they  wished  to  make  the  ridge 
4  inches  above  the  tops  of  the  sides.  Their 
problem  was  to  find  how  wide  to  order 
the  slanting  boards  for  the  top  of  the  hood. 
How  wide  should  they  be  in  order  to  leave 
no  waste? 

17.  A  girl  wished  to  put  up  a  window  shelf  for  flowers. 
The  distance  of  the  edge  of  the  board  from  the 
wall  is  10  inches  and  the  bottom  of  the  board 
is  15  inches  above  the  baseboard.  She  wanted 
to  cut  her  props  so  that  they  would  reach  from  the 
outer  edge  of  the  board  to  the  top  of  the  base- 
board. How  long  must  she  cut  her  props  on  the 
outside  edge  so  that  her  shelf  will  make  a  right 
angle  with  the  wall? 

18.  A  ladder  27  feet  long  leans  against  a  house 
from  which  its  base  is  separated  by  a  distance  of  18  feet. 
How  high  from  the  ground  is  the  top  of  the  ladder? 

19.  A  man  has  a  piece  of  land  in  the  shape  of  a  right  triangle. 
He  measures  the  two  legs  and  finds  them  to  measure  21  rods 
and  28  rods,  respectively.  Show  how  he  can  compute  the 
amount  of  fence  which  he  will  need  to  enclose  the  field,  without 
actually  measuring  the  other  side. 

20.  In  building  a  chicken  house  of  the 
dimensions  shown  in  the  diagram,  a  man 
wished  to  cover  the  top  with  ship-lap 
boards  which  were  to  extend  6  inches  over 
the  edges  at  each  end.  How  long  must  he 
order  his  boards  for  this  roof? 


250 


EIGHTH  YEAR 


21.  At  one  comer  of  a  level  rectangular  field  8  rods  long  and 
6  rods  wide  is  a  tower  165'  feet  high.  How  long  a  wire  will 
be  required  to  reach  from  the  top  of  the  tower  to  the  ground 
at  the  comer  diagonally  opposite? 

Note  that  you  must  use  two  right  triangles  to  solve  this 
problem. 

22.  In  the  figure  representing  the  end  of 
a  bam  you  find  the  dimensions  given. 
How  long  must  the  builder  order  his  rafters 
for  this  barn  if  he  wishes  them  to  project 
I  foot  at  the  eaves? 

23.  A  man  setting  a  telephone  pole  which 
projects  25  feet  above  the  ground  wishes  to 
brace  it  with  a  wire  attached  5  feet  from  the 

top  of  the  pole  to  a  stake  30  feet  from  the  base  of  the  pole. 
How  long  must  he  cut  his  wire  if  he  allows  3  feet  additional  for 
fastening  the  brace  at  both  ends? 

24.  Construct  very  accurately  a  right  triangle.  Then 
draw  accurate  squares  on  each  of  the  three  sides  as  shown 

in  the  illustration.  Extend 
the  sides  of  the  large  square 
as  shown  in  the  diagram 
and  draw  a  line  perpendicu- 
lar to  the  dotted  line,  as 
shown  in  the  square  on  the 
long  leg.  Number  the  parts 
of  the  small  squares  and 
cut  them  out.  If  you 
arrange  them  properly,  they 
will  cover  the  square  on  the  hypotenuse.  See  if  you  can  arrange 
them  in  the  right  order,  showing  that  the  sum  of  the  squares 
on  the  legs  is  equal  to  the  square  on  the  hypotenuse.  This  is  a 
practical  way  of  proving  the  principle  on  page  233. 


\ 

5 

PRACTICAL  MEASUREMENTS— PROBLEMS      251 


The  pitch  or  slant  of  the  roof  of  a  house  is 
found  by  dividing  the  height  above  the  eaves 
by  the  width  of  the  house.  In  the  illustration 
the  pitch  is  124-24,  or  §. 

26.  How  high  would  the  ridge  of  the  house 
be  above  the  eaves  to  give  a  pitch  of  f  ? 

26.  Find  the  length  of  a  rafter  for  a  house 
with  a  width  of  24  feet  and  a  pitch  of  f ,  allowing  1  foot  for  a 
projection  at  the  eaves. 

27.  The  pitch  of  a  house  30  feet  wide  is  ^.  Find  the 
length  of  a  rafter  for  this  roof,  allowing  1  foot  for  a  pro- 
jection at  the  eaves. 

A  carpenter  can  very  readily  determine  thje  length  of  a 

rafter  by  using  a  ruler  and  the  steel  square.     Along  one 

arm  of  the  square  he  lays  off  a  number  of  inches  equal  to 

the  number  of  feet  in  ^  of  the  width  of  the  house. 

Along  the  other  arm  he  lays  off  the  height  of  the 

ridge  above  the  eaves,  using  inches  to  represent 

feet.     A  ruler  joining  these  points  as  shown  in 

the  illustration  will  show  the  number  of  feet  in 

the  rafter. 

28.  Find  by  this  method  the  length 
of  a  rafter  for  a  house  24  feet  wide 
and  a  pitch  of  \. 


Equilateral  Triangles 

The  altitude  of  an  equilateral  triangle  is 
a  perpendicular  drawn  from  the  vertex  (C) 
to  the  base  (A  B).  The  altitude  divides 
the  equilateral  triangle  into  two  equal 
right  triangles.  Measure  A  D  and  D  B 
to  show  that  they  are  equal. 


252 


EIGHTH  YEAR 


Exercise  8 

1.  An  equilateral  triangle  has  each  of  its  sides  equal  to 
12  inches.    What  is  its  perimeter? 

2.  What  is  the  altitude  of  an  equilateral  triangle  with  each 
side  equal  to  10  inches? 

Solution:  Since  A  B  =  10  inches  and  A  D  =  D  B,  then  D  B  =  5 
inches.  In  the  right  triangle  D  B  C,  B  C  =  10  inches  and 
D  B  =  5  inches. 

102 _  52  =  100  -  25  =  75^    rpiie  square  on  C  D  must  be  75. 

C  D  then  is  the  square  root  of  75,  or  8.66+. 

Therefore:  The  altitude  of  an  equilateral  triangle  with  a 
side  of  10  inches  is  8.66+  inches. 

3.  Find  the  altitudes  of  the  following  equilateral  triangles 
and  fill  out  the  table  as  indicated : 


PROBunn 

Length  of  side,  or 

EQUILATERM.  TRIANGLE, 

LENGTH  or 

Altitude 

ALTlTUDt,  -r  SlOn  . 

1 

10 

8.66  + 

.866  + 

2 

IE 

? 

f> 

3 

8 

■? 

? 

4 

16 

■? 

? 

5 

6' 

? 

? 

4.  What  do  you  find  the  quotient  of  the  altitude  divided 
by  the  side  of  each  equilateral  triangle  to  be? 

Since  we  have  found  that  the  altitude  of  any  equilateral 
triangle  is  .866  of  the  side,  we  may  now  use  this  fact  and  save 
ourselves  a  great  deal  of  computation. 

5.  Find  the  altitude  of  an  equilateral  triangle  whose  side 
is  25  inches. 

Solution:    .866X25  inches=21.65  inches. 

6.  Find  the  area  of  an  equilateral  triangle  whose  side  is 
8  inches;  one  whose  side  is  5  inches. 


PRACTICAL  MEASUREMENTS— CIRCLES      253 


Circles 
A  circle  is  a  figure  bounded  by  a  curved 
line  every  point  of  which  is  at  a  given 
distance  from  a  point  within,  called  the 
center.  The  bounding  line  is  called  the  cir- 
cumference of  the  circle. 

A  straight  line  drawn  through  the  center 
of  the  circle  and  terminating  at  both  ends 
in  the  circumference  is  called  a  diameter  of  the  circle. 

The  distance  from  the  center  to  the  circumference  is  called 
the  radius  of  the  circle.  The  diameter  is  how  many  times 
as  long  as  the  radius? 


Class  Experiment 

The  problem  is:  To  find  the  ratio^  of  the  circumference  of 
any  circle  to  its  diameter. 

The  ratio  of  the  circumference  to  the  diameter  (C^D)  is 
known  as  yi  and  is  designated  by  the  Greek  letter  tt. 

Each  pupil  in  the  class  should  measure  very  carefully  the 
circumference  of  some  circular  object.  This  may  be  done  with  a 
tape  line  or  by  measuring  with  a  string  and  then  measuring  the 
length  of  the  string  with  a  ruler.  Then  measure  the  diameter 
of  the  same  object.  Next  divide  the  circumference  by  the 
diameter  and  carry  out  the  quotient  4  decimal  places. 

Enter  the  results  found  by  each  member  of  the  class  in  a 
table  similar  to  the  form  given  below,  reduced  to  decimals : 


Pupil. 

ClRCUMrCRCNCE, 

DiAMETCR 

ir=c^D. 

Rici-iARD  Roe 

4.125  in. 

1.3125  in. 

3.1428  + 

'The  ratio  of  one  number  to  another  is  the  number  of  times  the  first 
contains  the  second.  For  example,  the  ratio  of  8  to  4  is  the  number  of 
times  8  contains  4,  or  2. 


254  EIGHTH  YEAR 

Find  the  average  value  of  tt  for  all  the  pupils  in  the  class  and 
compare  the  value  which  you  have  found  with  the  accurate 
value  7r  =  3.1416. 

Since  x  is  the  quotient  of  the  circumference  divided  by  the 
diameter,  the  circumference  is  equal  to  the  diameter  multiplied 
by  TT, 

or  C  =  7rXD. 

Since  the  diameter  is  twice  the  radius,  C=7rX2  r,  or  27rr. 

In  formulas  the  sign  X  is  frequently  omitted,  but  the  expres- 
sion 27rr  is  understood  to  mean  2  X  tt  X  r.  It  is  much  shorter  to 
write  it  27rr. 

Exercise  9 

1.  Find  the  circumference  of  a  circle  whose  diameter  is 
8  inches. 

Solution:    C  =  7rD  =  3.1416X8  inches  =  25.1328  inches. 

2.  Find  the  circumference  of  circles  with  the  following 
diameters:     12  inches,  10  feet,  15  inches,  5  yards. 

3.  The  radius  of  a  circle  is  9  inches.    Find  the  circumference. 

4.  The  circumference  of  a  circle  is  50.2656  inches.  Since  tt 
is  already  known,  find  the  diameter  of  this  circle. 

6.  A  circular  flower  bed  is  8  feet  in  diameter.  How  many 
bricks  must  I  buy  in  order  to  put  a  border  of  bricks  around 
the  bed  1  brick  thick?   (A  brick  is  8  inches  long.) 

6.  A  farmer  builds  a  circular  bam  having  a  diameter  of 
40  feet.    What  is  the  length  of  the  circumference  of  the  barn? 

7.  The  Equator  of  the  earth  is  approximately  25,000  miles. 
What  is  the  equatorial  diameter  of  the  earth? 

8.  How  much  fringe  is  needed  to  trim  the  edge  of  a  circular 
lamp  shade  14  inches  in  diameter? 


PRACTICAL  MEASUREMENTS— SHOP  PROBLEMS    255 

9.  How  long  a  piece  of  tatting  would  it  take  to  edge  the 
cuffs  of  a  girl's  sleeves  if  the  cuffs  are  2f  inches  in  diameter? 

10.  A  farmer's  roller  is  32  inches  in  diameter.  How  many 
revolutions  will  the  roller  make  in  rolling  a  corn  row  a  quarter 
of  a  mile  long? 

11.  A  bicycle  has  wheels  28  inches  in  diameter,  outside 
measurement.  How  many  revolutions  will  each  wheel  make  in 
going  a  mile? 

12.  A  circular  wading  pool  40  feet  in  diameter  has  a  concrete 
side  walk  3  feet  wide  extending  around  the  border.  How  much 
longer  is  the  outside  circumference  of  this  walk  than  the  inside 
circumference? 

Exercise  10 


c^r~i^. 


1.  The  trough  of  a  pen  tray  is 
2  inches  wide.  How  wide  apart 
must  I  set  the  points  of  my  compass 
in  order  to  draw  the  semi-circle  at  each  end? 

2.  If  the  board  is  2f  inches  wide  and  the  end  of  the  trough 
is  to  be  §  inch  from  the  end,  locate  the  point  for  the  center  of 
the  semi-circle  at  each  end. 

3.  A  boy  in  the  forge  shop  wishes  to  make  a  ring  8  inches 
in  diameter  out  of  f -inch  stock.  Allowing  3  times  the  diameter 
of  the  rod  for  extra  in  welding,  how  long  must  he  cut  the 
piece  of  stock  to  make  this  ring? 

4.  How  long  must  a  rod  be  cut  out  of  f -inch  stock  to  make 
a  ring  18  inches,  inside  diameter?    Make  allowance  for  welding. 

6.  A  grindstone  36  inches  in  diameter  makes  40  revolutions 
per  minute.  What  is  the  cutting  speed  in  feet  per  minute  of 
this  stone?  (Find  the  number  of  feet  of  the  circumference  that 
will  pass  under  the  edge  of  a  tool  in  1  minute.) 


256 


EIGHTH  YEAR 


6.  Another  grindstone  in  the  shop  is  only  24  inches  in 
diameter.  How  many  revolutions  per  minute  must  it  make  to 
have  the  same  cutting  speed  as  the  grindstone  described  in 
Problem  5? 

7.  A  pulley  on  a  countershaft  in  a  shop  is  14 
inches  in  diameter.  How  many  inches  of  belt  will 
pass  over  this  pulley  in  one  revolution? 

8.  The  pulley  on  a  wood  lathe  is  6  inches  in 
diameter.  How  many  inches  of  belt  will  pass  over 
this  pulley  in  one  revolution? 

9.  How  many  revolutions  will  the  lathe  pulley 
make  for  one  revolution  of  the  pulley  on  the 
countershaft? 

10.  If  the  speed  of  the  countershaft  is  720 
revolutions  per  minute,  what  is  the  speed  of  the 
lathe? 

11.  If  you  have  a  shop  in  your  school,  visit  it  and  make 
other  problems  similar  to  the  ones  given  above 


Area  of  Circles 


When  a  circle  is 
cut  into  pieces  as 
shown  in  this 
i  Ilust  ration, 
the  pieces  are  al- 
most triangular  in 
shape,  the  bases 
being  slightly 


The  circle  divided  into  triangles 


curved.  If  we  arrange  these  triangles  in  a  row  with  half  of 
the  triangles  pointing  up  and  half  of  them  filling  in  the  spaces 
between  as  shown  in  the  diagram  on  the  next  page,  we  should 
have  approximately  a  parallelogram: 


PRACTICAL  MEASUREMENTS— CIRCLES        257 

The  base  of  this  parallelogram 
is  what  part  of  the  circumference 
of  the  circle? 

The  altitude  of  the  parallelogram  is  the  same  as  the  radius  of 
the  circle. 

Since  the  base  of  the  parallelogram  =  ^  of  the  circumference 
of  the  circle  (which  =  27rr),  the  base  of  the  parallelogram  =  ttt. 

The  area  of  the  parallelogram  =  base X altitude  or  7rrXr=7rr'. 

But  the  area  of  the  circle  is  the  same  as  the  area  of  the 
parallelogram.    Therefore  the  area  of  a  circle  =  7rr2. 

PRINCIPLE:    The  area  of  a  circle  is  equal  to  the  square  of 
the  radius  multiplied  by  TT.  Jt  ^        -- /T'  ' 

Exercise  11 

1.  Find  the  area  of  a  circle  8  inches  in  diameter. 

Solution:  Radius  of  circle  8  inches  in  diameter =4  inches. 
Area  of  circle =7rr2  =  3.1416X16  =  50.2656. 

Therefore  the  area  of  the  circle  =  50.2656  square  inches. 

2.  What  is  the  area  of  a  circle  with  a  radius  of  8  inches? 

3.  Find  the  area  of  a  circle  3  feet  in  diameter? 

4.  Find  the  area  of  the  8-inch  circle  in 
the  diagram  at  the  left.  Find  the  area  of  the 
12-iuch  circle.    Find  the  area  of  the  ring. 

5.  A  cow  is  tethered  to  a  stake  in  a  grass 
field  by  a  rope  100  feet  long  attached  to  one 
of  its  fore  feet.      What  is  the  area  in- 
cluded within  the  sweep  of  the  rope  around  the  stake? 

6.  If  the  rope  be  attached  to  one  of  the  hind  feet  of  the 
cow,  giving  the  animal  a  reach  of  five  feet  more  from  the  stake, 
how  much  additional  area  will  she  have  to  graze  over? 


258  EIGHTH  YEAR 

7.  A  circular  lake  three  miles  in  diameter  is  drained  until 
it  is  only  two  miles  in  diameter.  What  area  has  been  reclaimed 
by  the  receding  of  the  water?    Draw  diagram. 

8.  By  irrigation  from  a  central  artesian  well,  with  radiating 
ditches  extending  half  a  mile  in  each  direction,  a  circular  area 
of  arid  land  has  been  reclaimed.  How  many  acres  does  it 
contain?    Draw  diagram. 

9.  If  the  radiating  ditches  be  extended  to  twice  their  lengtli, 
what  will  be  the  gain  in  irrigated  area?    Draw  diagram. 

10.  Bottles  two  inches  in  diameter  are  packed  in  a  box  one 
foot  square,  inside  measure.  How  much  of  the  area  of  the 
bottom  of  the  box  is  covered  by  the  bottles?  Would  this  be 
the  same  if  there  were  but  one  bottle,  and  if  it  were  one  foot 
In  diameter?    Draw  diagram. 

11.  A  certain  revolving  searchlight  illuminates  the  land  to  a 
distance  of  five  miles.  What  area  is  included  in  the  circle  of 
its  illumination? 

12.  A  farmer  builds  a  circular  barn  having  a  diameter  of 
40  feet.  Its  circular  wall  will  have  3.1416  times  the  length  of 
the  diameter.  What  will  be  the  length  of  it?  Suppose  this 
length  of  wall  were  used  to  enclose  a  square.  What  would  be 
the  length  of  one  of  the  sides?  What  would  then  be  the  area 
of  the  bam?  \ 

13.  What  is  the  area  of  the  circular  barn?  What  is  the  gain 
in  area  from  having  the  barn  circular  in  form? 

14.  A  concrete  side  walk  3  feet  wide  surrounds  a  circular 
fountain  15  feet  in  diameter.  How  many  square  feet  are  there 
in  the  surface  of  the  walk? 

15.  How  many  3-inch  circles  for  jelly  glass  lids  can  be  cut 
from  a  rectangular  piece  of  tin  24  inches  wide  and  36  inches 
long?    How  many  square  inches  are  left  in  the  waste  pieces? 

Have  pupils  bring  to  class  other  practical  problems  on  circles. 


PRACTICAL  MEASUREMENTS— CIRCLES        259 

16.  The  square  in  the  figure  at  the  right  is  said  to  be  circum- 
scribed about  the  circle.    The  circle  is  said 

to  be  inscribed  in  the  square. 

If  the  side  of  the  square  is  12  inches, 
what  is  the  area  of  the  square? 

What  is  the  area  of  the  inscribed  circle? 

17.  Divide    the    area    of   the    inscribed 
circle  by  the  area  of  the  square.     If  your 

work  is  accurate,  the  result  should  be  .7854.    That  is,  the  area 
of  a  circle  is  .7854  of  a  square  with  a  side  equal  to  the  diameter. 

18.  From  this  fact  we  get  the  rule:     To  find  the  area  of  a 
circle  multiply  the  square  of  the  diameter  by  .7854. 

19.  Find  the  areas  of  circles  6  inches,  8  inches  and  12  inches 
in  diameter  by  this  rule. 

Exercise  12.    Review  of  Circles 

1.  How  many  square  feet  are  there  in  the  area  of  a  circular 
flower  bed  7  feet  in  diameter? 

2.  Two  girls  made  a  set  of  doilies  consisting  of  a  center- 
piece 18  inches  in  diameter  and  6  small  doilies  5  inches  in 
diameter.  How  many  inches  of  crochet  edging  did  they  have 
to  make  to  trim  all  the  doilies  in  that  manner? 

8.  How  many  square  inches  of  musUn  were  wasted  in  the 
squares  from  which  the  doilies  were  cut? 

4.  Find  the  area  of  a  circle  3  inches  in  diameter.  Find  the 
area  of  a  circle  6  inches  in  diameter.  The  area  of  the  second 
circle  is  how  many  times  the  area  of  the  first  cirde? 

5.  In  a  4-inch  steam  pipe  the  iron  is  :j  of  an  inch  thick. 
Find  the  area  of  the  opening  in  the  pipe. 

6.  Find  the  area  of  a  circular  flower  bed  8  feet  in  diameter. 
Find  its  circumference. 


260 


EIGHTH  YEAR 


7.  The  cold  air  inlet  for  a  furnace  should  have  the  same 
area  as  the  sum  of  the  areas  of  the  hot  air  pipes.  If  there  are 
six  6-inch  hot  air  pipes  leading  from  the  furnace,  what  should 
be  the  area  of  the  cold  air  inlet? 

8.  If  the  cold  air  inlet  is  rectangular  in  shape  and  has  a 
length  of  15  inches,  what  should  be  its  width  to  furnish  sufficient 
air  for  the  six  furnace  pipes? 

9.  A  circular  asbestos  pad  is  7§  inches  in  diameter.  How 
many  of  these  pads  can  be  made  from  a  piece  of  asbestos  padding 
30  inches  square?  Draw  a  diagram  to  show  the  arrangement 
of  the  circles. 

10.  How  many  square  inches  of  waste  material  would  be 
left  in  cutting  out  these  circular  pads  from  the  30-inch  square? 


Hexagons 

A  regular  hexagon  is  a  six-sided  figure  with  equal  sides  and 
equal  angles. 

A  regular  hexagon  may  be  inscribed  in  a 
circle  by  taking  the  compass  spread  to  the 
length  of  the  radius  used  in  drawing  the 
circle  and  marking  off  six  arcs  intersecting 
the  circumference  as  shown  in  the  figure  at 
the  left.  Then  join  the  six  points  of  division 
as  indicated  to  form  the  regular  hexagon. 


Exercise  13 

1.  Construct  a  regular  hexagon  with  a 
ruler  and  compass  as  directed  above. 

2.  Divide  the  regular  hexagon  into  six 
triangles  as  shown  in  the  figure  at  the  left. 

How  do  these  six  triangles  compare  in 
size?    Why? 


PRACTICAL  MEASUREMENTS— SOLIDS  261 

3.  Find  the  area  of  an  equilateral  triangle  with  a  side 
equal  to  6  inches.     (See  page  252.) 

4.  Since  the  six  equilateral  triangles  of  the  hexagon  are  all 
equal,  show  how  to  find  the  area  of  a  regular  hexagon. 

5.  Find  the  area  of  a  regular  hexagon  with  each  side  equal 
to  6  inches. 

6.  What  is  the  perimeter  of  the  regular  hexagon  described 
in  the  preceding  exercise? 

7.  Find  the  area  of  a  hexagon  with  a  perimeter  of  48  inches. 
Find  the  area  of  a  square  with  the  same  perimeter.  Also  find 
the  area  of  a  circle  with  a  circumference  of  48  inches.  Which 
figure  contains  the  greatest  area  for  the  given  perimeter? 

8.  Why  do  bees  have  hexagonal-shaped  cells?  Consider 
both  area  and  convenience  of  arrangement. 

Measurements  of  Solids 

We  have  been  studying  triangles,  rectangles,  trapezoids, 
hexagons,  circles,  etc.  All  of  these  figures  have  two  dimensions, 
length  and  breadth.  The  term  polygon  is  a  general  term, 
meaning  many-sided,  which  applies  to  all  of  these  figures. 

A  figure  which  has  three  dimensions,  length,  breadth  and 
thickness,  is  called  a  solid. 

The  term  solid  does  not  mean  that  the  figure  be  composed 
of  some  compact  material,  for  it  may  apply  equally  well  to  an 
empty  bin,  box  or  jar. 

There  are  certain  solid  figures  with  which  we  ought  to  be 
famiUar  because  we  see  them  about  us  in  daily  life. 

A  prism  is  a  soUd  having  two  bases  which  are  equal  and 
parallel  and  whose  lateral  (or  side)  faces  are  parallelograms. 
The  most  common  prisms  are  triangular  and  quadrangular. 


262 


EIGHTH  YEAR 


Triangular   Prism  Quadrangular   Prism 

Triangular  glass  prisms  are  used  for  bending  rays  of  light. 
They  are  used  in  some  forms  of  opera  glasses.  The  luxfer 
prisms  are  used  in  upper  parts  of  the  windows  of  large  rooms 
to  bend  and  throw  the  light  farther  across  the  room.  You 
will  find  how  a  prism  bends  a  ray  of  light  in  your  science  work. 

The  most  common  forms  of  quadrangular  prisms  are  rec- 
tangular solids  such  as  bins,  rooms  (rectangular  in  shape), 
boxes,  freight  cars,  bricks,  etc. 

Exercise  14.    Area  of  Surface  of  a  Prism 

In  finding  the  area  of  the  surface  of  a  prism,  we  are  using  no 
new  principles.  We  simply  find  the  areas  of  the  two  bases 
and  the  areas  of  the  lateral  surfaces  and  add  these  to  get  the 
total  surface  of  the  prism. 

1.  Find  the  total  surface  of  a  room  15  feet  long,  12  feet  wide 
and  10  feet  high. 

2.  What  is  the  area  of  the  surface  of  a  triangular  glass 
prism  3  inches  long  and  whose  bases  are  equilateral  triangles 
with  each  side  equal  to  1  inch? 

3.  What  is  the  area  of  the  surface  of  a  brick  8  in,  x  4  in.  x 
2  in.? 

4.  What  is  the  area  of  the  surface  of  a  rectangular  block  of 
wood  whose  length  is  4  feet  and  whose  bases  are  6  inches  square? 

6.  Find  the  number  of  square  inches  of  cardboard  in  a  box 
6  in.  X  3i  in.  X  if  in.  without  a  top. 


PRACTICAL  MEASUREMENTS— PRISMS       263 

Volumes  of  Prisms 

If  you  made  a  quadrangular  or  rectangular 
prism  out  of  inch  cubes  as  shown  in  the  figure 
which  is  3  inches  long,  3  inches  wide  and  3  inches 
high,  how  many  cubes  would  it  take  to  make  •■ 
one  row  along  the  bottom?  How  many  such  rows  are  there 
in  one  layer?  How  many  layers  are  there  in  the  prism?  How 
many  cubes  are  there  in  the  volume  of  the  prism?  How 
many  inch  cubes  are  there  in  the  volume  of  the  prism?  The 
volume  of  a  prism  is  generally  expressed  in  cubic  units,  though 
it  may  be  expressed  in  gallons,  barrels,  bushels,  and  various 
other  measures  which  are  made  up  of  a  certain  number  of  cubic 
units.    A  short  way  of  thinking  the  above  process  is: 

PRINCIPLE :    The  voliune  of  a  prism  is  the  product  of  the  area 
of  the  base  and  the  altitude. 

The  above  prism  is  a  cube,  which  has  6  equal  square  faces. 
The  volume  of  the  cube  is  equal  to  (3  X  3)  X  3,  or3'.  The  expres- 
sion 3'  is  read  3  cubed  and  means  that  the  volume  of  a  cube  is 
equal  to  the  cube  of  its  edge. 

Exercise  15 

1.  What  is  the  volume  of  a  rectangular  prism  12  inches  long, 
8  inches  wide  and  6  inches  high? 

2.  How  many  cubic  feet  are  there  in  a  box  4  feet  long, 
3  feet  wide  and  2§  feet  high? 

3.  How  many  cubic  inches  are  there  in  a  brick?  (A  brick 
is  8  J  inches  long,  4  inches  wide  and  2  j  inches  thick.) 

4.  How  many  cubic  inches  are  there  in  a  cubic  foot?  How 
many  bricks  would  make  a  cubic  foot  if  there  was  no  mortar 
between  them?  22  bricks  are  figured  as  making  a  cubic  foot 
of  wall.  How  many  bricks  are  saved  by  the  space  occupied 
by  the  mortar? 


264  EIGHTH  YEAR 

5.  An  excavation  for  a  house  is  40  feet  long,  32  feet  wide 
and  4  feet  deep.  How  many  loads  of  earth  were  removed? 
(1  cubic  yard  =  1  load.) 

6.  A  bin  is  20  feet  long,  8  feet  wide  and  6  feet  deep.  How 
many  bushels  of  wheat  will  it  hold?  (1  bushel  =  how  many 
cubic  inches?) 

7.  What  is  the  volume  in  cubic  feet  of  a  rectangular  horse 
trough  6  feet  long,  3  feet  wide  and  2^  feet  deep? 

8.  How  many  gallons  will  the  tank  in  Problem  7  hold? 
(1  cubic  foot  =  how  many  gallons?) 

9.  The  swimming  tank  in  a  certain  club  house  is  40  feet 
long,  20  feet  wide  and  has  a  uniform  depth  of  5  feet.  How 
many  gallons  of  water  are  there  in  this  tank? 

10.  A  freight  car  is  30  feet  long,  8^  feet  wide  and  4  feet  deep. 
How  many  tons  of  anthracite  coal  will  it  hold  if  1  ton  of  anthra- 
cite coal  occupies  34  cubic  feet  of  space? 

11.  A  rectangular  block  of  ice  is  30  inches  long,  24  inches 
wide  and  9  inches  thick.  How  much  will  it  weigh  if  a  cubic 
foot  of  ice  weighs  57.5  pounds? 

12.  An  excavation  for  a  house  contains  6000  cubic  feet. 
If  it  is  40  feet  long  and  30  feet  wide,  how  deep  is  it? 

13.  A  bin  22^  feet  long  and  6  feet  wide  must  be  how  deep 
to  contain  576  bushels,  estimating  the  bushel  at  1 J  cubic  feet? 

14.  A  wagon  box  is  found  to  have  the  following  inside 
measurements:  36  inches  wide,  26  inches  high  and  10  feet 
4  inches  long.  How  many  bushels  of  corn  on  the  cob  will  it 
hold  if  4000  cubic  inches  of  corn  on  the  cob  =  1  bushel? 

15.  A  rectangular  corn  crib  20  feet  long  and  12  feet  wide  is 
filled  with  ear  com  to  a  depth  of  10  feet.  How  many  bushels 
of  com  does  the  crib  hold? 


COMPUTING  RADIATION 


265 


Exercise  16.     How  to  Compute  Radiation 

In  computing  the  number  of 
square  feet  of  radiating  surface 
needed  for  any  room,  three  things 
are  taken  into  consideration:  (1)  the 
contents  in  cubic  feet;  (2)  the  num- 
ber of  square  feet  in  the  outside  or 
exposed  walls  and  (3)  the  area  of 
the  windows. 

1.  Find  the  steam  radiation  needed  for  a  room    15  feet 
long,  12  feet  wide  and  8^  feet  high,  one  exposed  wall  15  feet 
by  8^  feet  and  two  windows  5  feet  by  2§  feet, 
Cu.  ft.  in  contents  =  15  X  12  X  8^  =  1530. 
Sq.  ft.  in  exposed  wall  =  15  X  Sj  =  127i. 
Sq.  ft.  in  area  of  windows  =  2  X  5  X  2|  =  25. 

From  the  table  on  the  next  page  we  find  the  number  in  the  cubic  con- 
tents nearest  1530.  1500  is  the  nearest.  The  radiation  for  that  number 
of  cubic  feet  for  steam  is  15  square  feet.  Next  find  the  radiation  for  the 
exposed  wall.  127|  is  about  half  way  between  112  and  144  so  8  square 
feet  of  radiation  are  required  for  the  exposed  wall.  26  is  the  nearest  num- 
ber in  window  area  so  9  square  feet  are  required  for  this  factor.  The  total 
number  of  square  feet  required  for  steam  =  15+8+9=  32. 

The  number  of  square  feet  per 
section  of  a  standard  3  column  radi- 
ator is  shown  in  the  table  at  the 
left.  If  a  38  inch  radiator  was  used 
in  the  room  just  figured,  we  would 
need  as  many  sections  as  6  is  con- 
tained in  5^  or  6 1  sections.  7  sec- 
tions would  meet  the  requirements 
and  leave  a  little  margin.  If  we 
wish  to  compute  the  radiation  for 
20  degrees  below  zero,  we  must  add 
20%  (or  1%  for  each  degree  below  zero).  20%  X  32  =  6.4.  32  +  6.4 
=  38.4,  the  nimiber  of  square  feet  for  20  degrees  below  zero.  At  5  sq.  ft. 
per  section,  it  would  take  approximately  8  sections  for  that  temperature. 


Height  of  Radiator 
in  Inches 

Sq.  Ft.  per 
Section 

22 

3 

26 

3.75 

32 

4.5 

38 

5 

45 

6 

266 

EIGHTH 

YEAR 

Radiation  Table^ 

' 

Sq.  Ft.  of 

Sq.  Ft.  of 

Sq.  Ft.  of 

s 

3  O 

CO 

Radiation 

^1 

Radiation 

*i  O 

^5 

Radiation 

1 

a 

t 
^ 

1 

a 

j2 

1 
1 

s 

1 

CO 

a 

500 

8 

5 

6 

16 

2 

1 

1 

6 

3 

2 

2 

700 

12 

7 

9 

48 

5 

3 

4 

10 

5 

3 

4 

900 

15 

9 

11 

80 

8 

5 

7 

14 

7 

5 

5 

1100 

18 

11 

14 

112 

11 

7 

9 

18 

9 

6 

6 

1300 

21 

13 

16 

144 

15 

9 

12 

22 

11 

7 

8 

1500 

25 

15 

19 

176 

18 

11 

15 

26 

13 

9 

9 

1700 

28 

17 

21 

208 

21 

13 

17 

30 

15 

10 

10 

1900 

31 

19 

24 

240 

24 

15 

20 

34 

17 

11 

12 

2100 

35 

21 

26 

272 

27 

17 

23 

38 

19 

13 

13 

2300 

38 

23 

29 

304 

30 

19 

25 

42 

21 

14 

14 

2500 

41 

25 

31 

336 

34 

21 

28. 

46 

23 

15 

15 

2700 

44 

27 

34 

368 

37 

23 

31 

50 

25 

17 

17 

2900 

48 

29 

36 

400 

40 

25 

33 

54 

27 

18 

18 

3100 

52 

31 

39 

432 

43 

27 

36 

58 

29 

19 

20 

3300 

55 

33 

41 

464 

47 

29 

39 

62 

31 

21 

21 

3500 

58 

35 

44 

496 

50 

31 

41 

66 

33 

22 

22 

3700 

61 

37 

46 

528 

53 

33 

44 

70 

35 

23 

23 

3900 

65 

39 

49 

560 

56 

35 

47 

74 

37 

24 

25 

4100 

68 

41 

51 

592 

59 

37 

49 

78 

39 

26 

26 

4300 

71 

43 

54 

624 

63 

39 

52 

82 

41 

27 

28 

4500 

75 

45 

56 

656 

66 

41 

55 

86 

43 

29 

29 

4700 

78 

47 

59 

688 

69 

43 

57 

90 

45 

30 

31 

4900 

82 

49 

61 

720 

72 

45 

60 

94 

47 

31 

32 

iThese  figures  are  based  on  a  temperature  of  70°  F.  inside  and  0    out- 
side.    Add  1%  to  radiation  for  each  degree  of  difference. 

2.  Find  the  amount  of  radiation  needed  for  the  room  de- 
scribed on  the  preceding  page  if  hot  water  is  used.  How  many 
sections  of  22-inch  radiators  would  be  needed? 

3.  Compute  the  amount  of  radiation  needed  for  the  same 
room  if  a  vapor  system  of  heating  is  used.  How  many  38-inch 
sections  would  be  needed? 

4.  Find  the  number  of  38-mch  radiator  sections  needed  for 
steam  heat  in  a  living  room  20  feet  long,  12  feet  wide,  and  9| 
feet  high.  A  side  and  an  end  of  this  room  are  exposed  to  the 
weather.     There  are  3  windows  5  feet  by  2\  feet. 


COMPUTING  RADIATION  267 

6.  Find  the  number  of  22-inch  hot-water  sections  needed  in 
zero  weather  for  the  same  room.     (See  problem  4.) 

6.  Find  the  number  of  32-inch  sections  needed  for  zero 
weather  for  a  vapor  system  for  the  same  room.  (See  problem  4.) 

7.  Find  the  number  of  38-inch  sections  needed  for  steam  at 
20  degrees  below  zero  for  a  schoolroom  28  feet  long,  24  feet 
wide,  and  14  feet  high.  A  side  and  end  are 'exposed  and  the  area 
of  the  windows  is  approximately  one-fifth  of  the  area  of  the  floor. 

Suggestion :  For  cubic  contents  greater  than  the  numbers  given  in  the 
table,  use  a  proportional  amount.  The  cubic  contents  of  this  room 
=  9408  cu.  ft.     Double  the  radiation  for  4700  cu.  ft. 

8.  Find  the  number  of  26-inch  sections  needed  for  hot-water 
heating  at  zero  weather  for  each  of  the  rooms  in  the  house  shown 
on  page  283.  Study  the  floor  plan  for  dimensions  of  rooms, 
windows,  and  exposed  walls.  Figure  the  height  of  all  rooms  as 
9i  feet. 

9.  Compute  the  number  of  38-inch  sections  needed  for  steam 
at  20  degrees  below  zero  for  each  room  of  this  house. 

10.  How  many  32-inch  sections  are  needed  for  a  vapor  system 
for  10  degrees  below  zero  for  each  room  of  this  house? 

11.  Compute  the  steam  radiation  for  your  schoolroom  at  20 
degrees  below  zero.  How  many  radiators  would  you  have  for 
this  room?  What  height  would  you  order?  How  many  sec- 
tions would  be  needed  in  each  radiator? 

12.  Compare  your  results  with  the  actual  amount  of  radiation 
in  your  schoolroom. 

The  protection  of  hills,  trees,  shrubs,  etc.,  would  affect  the  warmth  of  a 
house.  Rooms  on  the  north  side  of  a  house  would  also  be  colder  than 
those  with  a  southern  exposure.  Well  built  houses  are  also  warmer  than 
those  not  designed  for  protection  against  cold  weather.  Allowance  should 
be  made  for  all  of  these  factors  in  determining  the  radiation  for  a  room. 
The  figures  given  in  the  table  are  for  average  conditions. 


268  EIGHTH  YEAR 

Cylinder 

A  cylinder  is  a  solid  bounded  by  a  uniformly 
curved  surface  and  two  parallel  circular  bases. 

The  cylinder,  on  account  of  the  small  amount 
of  material  in  its  walls,  is  one  of  the  most  common 
of  the  solid  forms  in  practical  use.  Cisterns,  stove 
pipes,  water  pipes,  hot  water  tanks,  boilers  and 
^      ^^       silos  are  usually  cylindrical  in  shape. 

PRINCIPLE:    The  volxune  of  a  cylinder  is  equal  to  the  area  of 
the  circular  base  multiplied  by  the  altitude  (or  height). 

Exercise  17 

1.  Find  the  volume  of  a  cylinder  whose  base  is  6  inches  in 
diameter  and  whose  altitude  is  20  inches. 

2.  A  cistern  is  6  feet  in  diameter  and  8  feet  deep.  How 
many  gallons  of  water  will  it  hold?    (1  cubic  foot  =  7.5  gallons.) 

3.  A  barber  once  gave  me  this  problem.  "I  have  a  hot-water 
tank  14  inches  in  diameter  and  60  inches  high.  How  many 
gallons  of  water  does  it  hold?"  What  answer  should  I  have 
given  him? 

4.  A  farmer  has  a  silo  12  feet  in  diameter  and  35  feet  high. 
How  many  tons  of  silage  will  it  hold,  counting  34  pounds  to 
the  cubic  foot? 

5.  A  cylindrical  boiler  is  3  feet  in  diameter  and  12  feet 
long.    If  it  is  half  full  of  water,  how  much  water  does  it  contain? 

6.  A  bushel  measure  contains  2150.42  cubic  inches.  If  it 
is  12  inches  in  diameter,  how  high  is  it? 

7.  A  cylindrical  bucket  8  inches  in  diameter  and  15  inches 
high  will  nold  how  many  gallons? 

8.  Bring  to  class  for  solution  any  problems  you  can  find 
on  the  volumes  of  cylinders,  such  as  gasoline  tanks,  cisterns, 
standpipes,  stock  watering  tanks,  etc. 


PRACTICAL  MEASUREMENTS— THE  SILO      269 


The  Silo 

The  silo  is  one 
of  the  chief  factors 
in  successful  dairy- 
ing and  cattle  rais- 
ing. It  is  usually 
filled  with  com,  the 
stalks  and  ears  be- 
ing chopped  up 
while  still  green. 

To  secure  the 
pressure  necessary 
for  the  best  preser- 
vation of  silage,  the  silo  should  be  of  a  height  equal  to  at  least 
twice  its  diameter.  The  greater  the  height  of  the  silo,  the 
greater  will  be  the  weight  of  the  silage  and  the  more  it  will  be 
compressed.  The  cylindrical  form  allows  the  greatest  area  in 
proportion  to  the  wall  space  and  also  offers  less  friction  in  the 
settling  of  the  silage. 


Exercise  18 

1.  If  the  silo  in  the  above  illustration  is  14  feet  in  diameter 
and  filled  to  a  depth  of  28  feet,  what  is  the  total  weight  of  the 
silage,  the  average  weight  being  38  pounds  per  cubic  foot? 

2.  How  many  days  will  this  silage  last  a  herd  of  20  cows, 
allowing  each  cow  35  pounds  each  day? 

3.  How  long  will  a  silo  15  feet  in  diameter  and  filled  to  a 
depth  of  32  feet  feed  a  herd  of  30  cattle,  allowing  1  cubic  foot 
of  silage  for  each  head? 

4.  In  order  to  prevent  silage  from  spoiUng,  a  layer  1  ^  inches 
deep  must  be  fed  each  day.  If  my  silo  is  12  feet  in  diameter 
and  filled  to  such  a  depth  that  it  weighs  36  pounds  per  cubic 


270 


EIGHTH  YEAR 


foot,  how  many  cows  should  I  keep  to  feed  a  layer  of  that 
depth,  allowing  each  cow  38  pounds  each  day? 

The  weight  of  silage  varies  from  about  32  pounds  per  cubic 
foot  for  18  feet  in  depth  to  about  43  pounds  per  cubic  foot  for 
a  depth  of  36  feet. 

6.  A  certain  silo  is  14  feet  in  diameter  and  is  filled  with  silage 
to  a  depth  of  25  feet.  If  the  silage  weighs  36  f  pounds  per 
cubic  foot,  what  is  the  amount  of  it  in  tons? 

6.  How  long  will  this  silage  last  a  herd  of  24  cows,  allowing 
each  cow  40  pounds  each  day? 

7.  I  wish  to  build  a  silo  large  enough  to  supply  a  herd  of 
20  cows  for  190  days.  Plan  the  dimensions  for  a  cylindrical 
silo,  allowing  about  1  cubic  foot  per  day  for  each  cow.  (See 
Problem  4  for  minimum  depth  that  must  be  fed  each  day  to  keep 
the  silage  from  spoiling.) 

IRRIGATION 


Elephant  Butte  Dam,  New  Mexico 

The  Elephant  Butte  Dam,  built  across  the  Rio  Grande 
River  in  New  Mexico  by  the  United  States  Reclamation  Service, 


IRRIGATION  271 

is  1250  feet  long  and  200  feet  high.  It  is  18  feet  wide  at  the  top 
and  215  feet  wide  at  the  bottom.  610,000  cubic  yards  of 
masonry  were  used  in  the  construction  of  this  immense  dam. 

Water  for  irrigation  is  measured  by  the  acre-foot,  which  is 
the  amount  of  water  necessary  to  cover  an  acre  to  a  depth  of 
one  foot. 

r 

Exercise  19 

1.  An  acre-foot  is  equal  to  how  many  cubic  feet  of  water? 

2.  The  storage  capacity  of  the  Elephant  Butte  Reservoir 
is  2,642,292  acre-feet.  This  is  equal  to  how  many  cubic  feet 
of  water? 

3.  What  is  the  storage  capacity  in  gallons  of  this  reservoir? 

4.  The  state  of  Connecticut  has  an  area  of  4965  square 
miles.  How  deep  would  the  water  stored  in  the  Elephant 
Butte  Reservoir  cover  an  area  equal  to  the  state  of  Connecticut? 

6.  The  water  surface  of  this  reservoir  is  42,000  acres.  Find 
the  average  depth  of  water  in  the  reservoir. 

6.  The  Roosevelt  Dam  in  the  Salt  River  Valley  of  Arizona 
stores  up  1,284,200  acre-feet.  The  surface  of  this  reservoir  is 
16,329  acres.    What  is  the  average  depth  of  the  reservoir? 

7.  It  is  estimated  that  27,000  horse  power  of  electric  energy 
can  be  developed  from  the  water  in  the  Roosevelt  Reservoir. 
If  this  energy  is  worth  $50  per  horse  power  per  year,  how  much 
revenue  would  this  yield  per  year  if  it  were  all  used? 

8.  A  weir  (a  device  for  measuring  the  amount  of  water) 
shows  that  a  certain  box  in  an  irrigation  canal  is  delivering 
water  at  the  rate  of  2  cubic  feet  per  second.  How  long  will  it 
take  to  irrigate  40  acres  of  land,  supplying  f  of  an  acre-foot  per 
acre? 


272 


EIGHTH  YEAR 


9.  Land  was  offered  in  the  Salt  River  Valley,  Arizona,  at 
per  acre  before  the  Roosevelt  Dam  was  built.  Unimproved 
land  sold  at  about  $100  per  acre  after  the  irrigation  system 
was  completed.  The  area  of  the  completed  system  is  250,000 
acres.  Find  the  increase  in  the  value  of  the  land  as  a  result  of 
the  building  of  this  dam. 

10.  A  farmer  raised  8  tons  of  alfalfa  hay  per  acre  on  irrigated 
land  worth  $200  per  acre.  He  sold  this  hay  at  $10  per  ton.  If 
his  expenses  were  $25  per  acre,  what  were  his  profits  on  a  field 
of  20  acres  of  alfalfa?  What  per  cent  was  this  on  the  value  of 
the  land? 

11.  A  truck  farmer  planted  a  lO-acre  irrigated  tract  in  pota- 
toes on  Feb.  10.  He  harvested  this  crop  on  May  10,  making 
a  profit  of  $100  per  acre.  On  July  25  he  planted  corn  and  in 
the  autumn  of  that  year  sold  the  roasting  ears  so  as  to  yield 
a  profit  of  $60  an  acre.  What  was  the  total  profit  on  the  10- 
acre  tract  for  that  year? 

12.  Find  other  examples  of  irrigation  projects  and  make 
problems  similar  to  the  ones  in  this  exercise. 


GOOD  ROADS 


The  Lincoln  Highway 

When  the  Lincoln  Highway  is  finished  from  New  York  to 
San  Francisco,  it  will  be  a  magnificent  and  useful  memorial  to 
the  great  president  for  whom  it  was  named.  This  road  is 
planned  to  be  concrete  throughout  its  entire  length  of  over 
3000  miles. 


GOOD  ROADS 


273 


Exercise  20 

1.  In  1916  the  distance  on  the  Lincoln  Highway  from  New 
York  to  San  Francisco  was  3331  miles.  How  many  days  will 
it  take  a  touring  party  to  make  the  journey  if  they  drive  8 
hours  per  day  at  an  average  speed  of  15  miles  per  hour? 

2.  The  distance  from  Boston  to  New  York  by  road  is  234 
miles.  How  far  is  it  from  Boston  to  San  Francisco  by  way  of 
the  Lincoln  Highway? 

3.  Of  the  distance  from  New  York  to  western  Indiana, 
659  of  the  802  miles  of  the  Lincoln  Highway  are  hard  roads. 
How  much  will  it  cost  to  complete  the  rest  of  this  section  of  the 
road  at  $12,000  a  mile? 

4.  If  the  average  cost  for  concrete  roads  is  $13,000  per  mile, 
what  will  be  the  total  cost  of  the  Lincoln  Highway  from  New 
York  to  San  Francisco  when  completed? 

6.  Mention  other  important  state  and  national  highways 
with  which  you  are  familiar. 


Exercise  21.    The  Construction  of  Good  Roads 

1.  The  maximum  grade 
of  ascent  or  descent  for  im- 
portant roads  has  been 
fixed,  generally,  at  5%,  or 
5  feet  of  rise  or  fall  in  100 
feet  of  length.  For  a  rise 
of  528  feet,  what  would  be 
the  length  of  road,  at  this 
maximum  grade? 

2.  Gutter  grades,  at  the 
sides  of  roadways,  should 
have  a  minimum  fall  of  6  inches  in  100  feet  to  the  culverts. 
If  the  culverts  are  600  feet  apart,  how  much  will  the  gutters 
slope  to  meet  them  at  this  minimum  fall? 


Courtesy  Lincoln  Highway  Association 


274  EIGHTH  YEAR 

3.  For  a  road  15  feet  or  less  in  width,  the  middle  line,  or 
crown,  should  be  5  j  inches  higher  than  the  sides.  For  a  greater 
width  of  road,  the  crown  should  be  raised  ^  inch  for  each  foot 
of  distance  from  the  boundary.  What  should  be  the  height 
of  the  crown  of  a  road  18  feet  wide? — 24  feet  wide? 

4.  A  road  commission  found  that  26,509  square  yards  of 
concrete  roads  cost  $23,154.  If  the  roads  averaged  15  feet  wide, 
find  the  average  cost  per  mile  of  the  concrete  roads  in  that 
locality. 

6.  The  same  commission  found  that  13,699  square  yards  of 
brick-paved  roads  cost  $20,294.  Find  the  cost  of  brick  pave- 
ment per  mile  for  an  18-foot  surface. 

6.  651,123  square  yards  of  macadam  roads  were  found  to 
cost  $401,470.  Find  the  cost  per  mile  of  a  15-foot  macadam 
road. 

7.  A  tar  binder  is  often  placed  on  macadam  roads  to  hold 
the  fine  particles  of  crushed  stone  together.  About  2  gallons 
are  required  for  each  square  yard.  If  the  binder  costs  8  cents 
per  gallon,  what  will  be  the  cost  of  the  binder  for  a  mile  of 
macadam  road  15  feet  wide? 

8.  The  earth  work  on  a  certain  road  averaged  about  5560 
cubic  yards  per  mile.  Find  the  cost  of  this  earthwork  at  28.5 
cents  per  cubic  yard. 

9.  In  building  a  burnt-clay  road  in  the  South  for  300  feet 
as  a  test,  the  following  expenses  were  incurred : 

30^  cords  of  wood  at  $1.30  per  cord; 
20  loads  of  bark,  chips,  etc.  at  30  cents  per  load; 
Expenses  for  labor  and  teams — $38.30. 
What  was  the  cost  of  the  300-foot  road?    What  would  a 
mile  of  this  road  cost  at  the  same  rate? 

10.  If  a  ton  of  broken  rock  for  a  macadam  road  will  cover 
3.13  square  yards  of  surface,  how  many  tons  of  this  material 


GOOD  ROADS  275 

will  be  required  for  a  macadam  road  a  mile  long  and  15  feet 
wide  covering  it  to  the  same  depth? 

11.  A  county  road  commission  decides  to  build  4  miles  of 
macadam  roads  each  year  at  an  estimated  average  cost  of 
$7600  per  mile.  The  state  pays  ^  of  this  expense.  If  the 
assessed  valuation  of  the  county  is  $3,800,000,  what  will  be 
the  tax  rate  for  hard  roads  in  this  county? 

r-  ■  v-o"- .; /e'-o- ^ — -^o"—  — T 

Cross  Section  of  a  Concrete  Road 

Concrete  for  road  purposes  should  consist  of  a  mixture  of 
1  part  of  cement  to  2  parts  of  sand  to  3|^  parts  of  gravel  or 
crushed  stone. 

12.  The  cross  section  of  the  concrete  road  shown  in  the 
diagram  shows  the  concrete  to  be  6  inches  thick.  How  many 
cubic  yards  of  concrete  are  there  in  a  mile  of  this  road? 

13.  The  crown  of  this  road  shows  a  fall  of  3  inches  in  half 
the  width  of  the  road.     Find  the  fall  per  foot. 

14.  Under  each  edge  of  the  concrete  a  longitudinal  drain 
ditch  is  dug  and  filled  with  loose  stone.  How  many  cubic 
yards  of  stone  will  it  take  to  fill  a  mile  of  these  ditches  if  they 
are  8"xl0"? 

16.  How  much  stone  will  it  take  to  fill  120  lateral  drains  for 
each  side  of  the  road  per  mile,  the  drains  being  8"xl0"xl0'? 

16.  How  much  would  the  stone  cost  for  both  longitudinal 
and  lateral  drains  at  $1.00  per  cubic  yard? 

17.  How  much  would  it  cost  to  haul  this  stone  at  50  cents 
per  cubic  yard? 

18.  How  much  would  the  concrete  cost  for  a  mile  of  this  road 
at  $6.00  per  cubic  yard? 


276 


EIGHTH  YEAR 


Mr.  Davis  lives  2  miles  from  a  hard  road  on  which  there  is 
no  grade  exceeding  5%.  A  certain  city,  where  he  markets  his 
produce,  is  located  on  the  hard  road  6  miles  from  the  point 
where  his  branch  road  meets  the  hard  road.  Mr.  Davis  sold 
his  crop  of  1260  bushels  of  wheat  to  a  firm  in  the  city. 

19.  The  road  leading  from  his  farm  to  the  good  road  was  so 
rough  and  hilly  that  he  could  only  haul  18  two-bushel  sacks 
of  wheat  to  a  load.  How  many  such  loads  would  he  have  had 
to  haul  to  market  the  wheat  in  this  manner? 

20.  If  he  had  hauled  two  loads  per  day,  what  would  have 
been  the  cost  of  hauling  in  this  way,  counting  Mr.  Davis  and 
his  team  as  worth  $4.00  per  day?    Find  the  cost  per  bushel. 

21.  On  the  good  road  a  team  could  haul  35  sacks  of  2  bushels 
each  at  a  load.  Had  the  good  road  extended  to  his  farm,  what 
would  have  been  the  cost  of  marketing  the  wheat  at  $4.00  per 
day  for  2  loads?    Find  the  cost  per  bushel. 

22.  Compare  the  cost  per  bushel  for  hauling  on  a  good  road 
with  the  cost  per  bushel  on  the  unimproved  road. 

23.  Mr.  Davis  decided  to  hire  an  extra  team  to  haul  sacks 
from  his  farm  to  be  transfered  to  his  wagon  at  the  hard  road. 
He  then  hauled  the  large  loads  from  that  point  to  the  city.  By 
this  system  they  marketed  the  wheat  in  6  days.  At  $4.00  per 
day,  for  each  team,  find  the  cost  of  marketing  the  wheat  in 
this  way. 

24.  How  much  was  saved  over  the  method  described  in 
Problem  19? 


PRACTICAL  MEASUREMENTS— FARM  PROBLEMS  277 

Exercise  22 

Problems  Prepared  by  a  Farmer 

1.  I  sold  my  neighbor  a  crib  of  corn  20  feet  long,  9  feet 
4  inches  wide  and  10  feet  2  inches  high.  How  many  bushels 
of  com  were  in  this  crib,  counting  4000  cubic  inches  to  the 
bushel? 

2.  A  neighbor  asked  me  to  help  him  measure  three  cribs 
of  corn  which  he  had  sold.  We  found  the  cribs  to  measure  as 
follows: 

Crib  1—9  ft.  3  in.  long,  9  ft.  1  in.  wide,  8  ft.  5  in.  high. 

Crib  2—9  ft.  3  in.  long,  8  ft.  11  in.  wide,  8  ft.  4  in.  high. 

Crib  3—9  ft.  4  in.  long,  8  ft.  11  in.  wide,  8  ft.  4  in.  high. 
How  many  bushels  were  there  in  the  three  cribs?  (4000  cubic 
inches=l  bushel.) 

3.  How  many  bushels  of  com  are  there  in  a  frame  crib 
20  feet  long,  10  feet  wide  and  9  feet  high  if  there  are  20  studding 
2'^x4"x9  feet  long  to  be  deducted  from  the  contents  on  account 
of  being  on  the  inside  of  the  crib? 

4.  I  sold  20  wagon  loads  of  com  to  be  measured  in  wagons, 
counting  4000  cubic  inches  per  bushel.  How  many  bushels 
were  there  in  the  20  loads  if  the  wagon  box  was  10  feet  6  inches 
long,  3  feet  1  inch  wide  and  2  feet  1  inch  high? 

6.  How  many  tons  of  hay  are  there  in  a  mow  36  feet  long, 
14  feet  wide  and  17  feet  high,  allowing  512  cubic  feet  per  ton? 

6.  I  sold  a  stack  of  hay  which  was  24  feet  long,  14  feet  wide 
and  had  an  average  height  of  15  feet.  How  much  did  I  receive 
for  the  hay  at  $10  per  ton?    (Allow  512  cubic  feet  per  ton.) 

7.  How  many  tons  of  hay  are  there  in  a  mow  32  feet  6  inches 
long,  12  feet  8  inches  wide  and  14  feet  high? 


278 


EIGHTH  YEAR 


Measuring  Lumber 

In  buying  lumber  for  building 
a  house,  a  barn,  a  garage,  or  a 
shed  one  should  know  how  to 
check  the  amount  of  the  lumber 
and  know  where  the  different 
kinds  of  lumber  are  used. 

In  measuring  full-sized  boards 
or  timbers  the  following  method 
for  finding  the  number  of  board 
feet  will  be  found  to  be  the 
most  practical: 

Number  of  boards  X  length  in 
feet  X  width  in  inches  X  thick- 
ness in  inches  divided  by  12. 
Lumber  less  than  an  inch  in  thickness  is  counted  as  an  inch  thick . 

Exercise  23 

In  building  the  house  shown  in  the  above  plan,  the  following 
lists  of  boards  and  timbers  comprise  a  portion  of  the  lumber 
used.     Find  the  number  of  board  feet  for  each  line: 


1. 

No.  of  Pieces 
1 

Thickness 

6" 

Width 

8" 

Length 

8' 

Purpose 

Girder 

2. 

2 

6" 

8" 

9' 

Girder 

3. 

1 

6" 

8" 

12' 

Girder 

4. 

2 

6" 

8" 

14' 

Girder 

5. 

10 

6" 

6" 

6' 

Girder  posts 

A  girder  is  a  heavy  timber  used  to  support  the  first-floor  joists. 
They  are  supported  by  posts  in  the  basement,  called  girder  posts. 

6.  3  pieces  2"  X    6"  X  12'         Sill  plate 

7.  3  pieces  2"  X    6"  X  14'        Sill  plate 

8.  4  pieces  2"  X    6"  X  16'         Sill  plate 

The  sill  plates  are  the  timbers  which  rest  on  the  top  of  the 
foundation  walls. 


PRACTICAL.    LUMBER  MEASUREMENTS      279 

9.  280  pieces  2"  X    4"  X  9'       Studding. 

10.  52  pieces  2"  X    4"  X  6'         Studding. 

11.  74  pieces  2"  X    4"  X  8'         Studding. 

The  studding  are  the  upright  timbers  comprising  the  main 
portion  of  the  framework  of  a  house. 

12.  32  pieces  2"  X  4"  X  14'         Outside  plate. 

13.  51  pieces  2"  X  4"  X  14'         Inside  plate. 

A  plate  is  a  timber  resting  on  the  top  of  the  studding. 

14.  29  pieces  2"  X  10"  X  10'        First-floor  joist  and  box  sills. 

15.  28  pieces  2'^  X  10"  X  12'       First-floor  joist  and  box  sills. 

16.  32  pieces  2"  X  10"  X  14'        First-floor  joist  and  box  sills. 

17.  3  pieces  2"  X  10"  X  16'       First-floor  joist  and  box  sills. 

18.  11  pieces  2"  X    8"  X    9'       Second-floor  joists. 

19.  12  pieces  2"  X    8"  X  10'       Second-floor  joists. 

20.  14  pieces  2"  X    8"  X  12'       Second-floor  joists. 

21.  40  pieces  2"  X    8"  X  14'       Second-floor  joists. 
Joists  are  timbers  which  support  the  floors. 

22.  32  pieces  2"  X    6"  X  12'     Rafters. 

23.  26  pieces  2"  X    6"  X  22'     Rafters. 

24.  20  pieces  2"  X    6"  X  24'     Rafters. 
Rafters  are  the  slanting  timbers  which  support  the  roof. 

In  billing  lumber  the  lengths  of  some  of  the  different  boards 
are  not  specified,  but  the  total  length  in  linear  feet  is  given. 

26.  Find  the  number  of  board  feet  in  234  linear  feet  of  1"  by 
8"  boards  used  for  the  base  and  frieze  of  this  house. 

26.  How  many  board  feet  are  there  in  360  linear  feet  of  1"  by 
6"  boards  used  for  bracing? 

27.  Find  the  number  of  board  feet  in  5,240  linear  feet  of 
^"  by  6"  cypress  siding. 

Additional  work  on  lumber  measure  may  be  provided  by 
getting  local  prices  on  these  different  boards  and  timbers  and 
estimating  costs  as  well  as  the  number  of  board  feet. 


280 


EIGHTH  YEAR 


Practice  Exercises  in  Measurements 

These  exercises  involve  a  knowledge  of  the-  facts  and  principles  of 
measurements  as  well  as  an  abihty  to  compute  rapidly.  If  the  pupils  are 
not  able  to  give  the  facts  or  solve  the  problems  in  the  required  time  limits, 
they  should  be  drilled  until  they  can  do  so.  Use  the  following  time  hmits 
for  these  exercises: 

Excellent — 1^  minutes;  Good — 2  minutes;  Fair — 2^  mniutes. 
Exercise  A 


Fill  in  the 

1.  1  rod  = 

2.  1  day  = 

3.  1  yard  = 

4.  1  mile  = 

5.  1  quart  = 

6.  1  pound 

7.  1  peck  = 

8.  1  minute 

1  acre  = 

1  bushel 

1  foot  = 

1  gross  = 

1  sq.  yd. 

14.  1  cu.  yd. 
16.  1  mile  = 


following  blanks: 

feet. 

hours. 

—  feet. 

—  feet. 

—  pints. 

—  ounces. 


16.  1  dozen  =  things. 

17.  1  ton  =  pounds. 

18.  1  bushel  =  pecks. 

19.  1  cord  =  cu.  ft. 

20.  1  gallon  =  cu.  in. 


21.  1  week 


quarts, 
seconds. 


9 
10 
11 
12 
13 


sq.  rd. 
cu.  in. 


inches. 

—  things. 

—  sq.  ft. 

—  cu.  ft. 
■  yards. 


22. 
23. 
24. 
25. 
25. 
27. 
28. 
29. 
30. 


1  yard  =  — 
1  hour  =  — 
1  mile  =  — 
1  cu.  ft.  =  ■ 
1  ream  =  - 
1  rod  =  — 
1  gallon  = 
1  sq.  mi.  = 
1  sq.  ft.  =  - 


-  days. 

-  inches, 
minutes, 
rods. 

-  cu.  in. 


—  sheets, 
yards. 

—  quarts. 

—  acres. 

—  sq.  in. 


Exercise  B 

Find  the  areas  of  the  following  figures: 

1.  Rectangle:     16  feet  long  and  12§  feet  wide. 

2.  Parallelogram:     base  12  inches;  altitude  7f  inches. 

3.  Triangle:    base  40  rods,  altitude  30  rods. 

4.  Square  with  a  side  of  80  rods. 

6.  Trapezoid:    bases  18  in.  and  12  in.;  altitude  9  in. 
6.  Circle  with  a  diameter  of  10  inches. 


PRACTICE  EXERCISES  IN  MEASUREMENTS  281 

Exercise  C 

Find  the  area  of  these  figures : 

1.  Square  with  a  side  of  15  inches. 

2.  Circle  with  a  radius  of  40  feet. 

3.  Triangle:    base  11  inches;  altitude  8  inches. 

4.  Trapezoid:    bases  80  rd.  and  60  rd.;  altitude  40  rd. 

5.  Parallelogram:    base  15  feet;  altitude  10  feet. 

6.  Rectangle :    80  rods  long  and  60  rods  wide. 

Exercise  D 
Find  the  volume  of: 

1.  A  room  12  feet  long,  9  feet  wide,  and  8^  feet  high. 

2.  A  tank  8  feet  long,  3  feet  wide,  and  2§  feet  high. 

3.  A  bin  18  feet  long,  7  feet  wide,  and  6  feet  high. 

4.  A  cube  with  an  edge  of  8  inches. 

Exercise  E 
Find  the  volume  of : 

1.  A  silo  12  feet  in  diameter  and  28  feet  high. 

2.  A  cube  with  an  edge  of  7  inches. 

Exercise  F 

Find  the  number  of  board  feet  in : 

1.  Two  boards  1  inch  thick,  8  inches  wide,  and  12  feet  long. 

2.  Four  timbers  2  inches  thick,  6  inches  wide,  and  16  feet  long. 

3.  Five  boards  1  inch  thick,  4  inches  wide,  and  12  feet  long 

4.  Two  timbers  2  inches  thick,  4  inches  wide,  and  18  feet  long 

Exercise  G 

1.  How  many  cords  of  wood  are  there  in  a  pile  16  feet  long, 
6  feet  high,  and  4  feet  wide? 

2.  How  many  cubic  yards  of  material  are  there  in  a  wall  40 
feet  long,  5  feet  high,  and  1  foot  thick? 

3.  How  many  tons  of  coal  are  there  in  a  bin  12  feet  long,  6 
feet  wide,  and  5  feet  deep,  allowing  36  cubic  feet  to  a  ton? 


CHAPTER  V 
EFFICIENCY  IN  THE  HOME 


A  Southern  Colonial  Bungalow^ 

When  one  decides  to  build  a  house,  he  is  interested  in  seeing 
two  things:  an  exterior  view  of  the  finished  house  and  a  floor 
plan,  showing  the  arrangement  and  sizes  of  the  various  rooms. 

The  floor  plan  of  the  Southern  Colonial  Bungalow  is  shown  in  the 
illustration  on  the  next  page. 

Exercise  1.    A  Study  of  the  Floor  Plan 

1.  What   are    the    outside    measurements    of   the    house, 
excluding  the  front  porch? 

2.  Read  the  sizes  of  the  various  rooms  from  the  floor  plan. 

3.  How  large  is  the  front  porch? 

4.  How  many  chimneys  are  shown  in  the  plan? 

6.  Would  you  make  any  changes  in  the  plan  if  you  were 

going  to  build  this  house? 

'Acknowledgment  is  made  to  the  "Gordon -Van  Tine  Homes,"  Daven- 
port, Iowa,  for  the  illustrations  here  given  (also  on  p.  121),  and  for  the 
reUable  data  on  which  these  problems  are  based. 

282 


EFFICIENCY  IN  THE  HOME 


283 


Exercise  2.    Cost  of  the  House 

1.  The  basement  excavation  was  1.8  yards  deep.  Find 
the  number  of  cubic  yards  of  earth  that  was  excavated.  See 
the  floor  plan  for  the  dimensions  of  the  house.  The  basement 
is  the  same  size  as  the 
house,  exclusive  of  the  front 
porch. 

2.  In  excavating  for  the 
basement  of  the  house, 
there  were  200  cubic  yards 
of  earth  removed.  Find  the 
cost  of  excavating  at  25 
cents  per  cubic  yard. 

3.  In  the  foundation  the 
following  materials  were 
used:  42  perch^  of  stone 
at  $5.00  per  perch;  40 
cubic  yards  of  poured  con- 
crete at  $5.50  per  cubic 
yard;  and  block  and  foot- 
ings costing  $195.  Find  the 
total  cost  of  the  foundation. 

4.  The    contractor 
charged    for     120    square 
yards  of  cement  floor  at  80 
cents  per  square  yard.    Find  the  cost  of  cementing  the  base- 
ment. 

6.  The  plastering  was  estimated  at  600  square  yards  at 
35  cents  per  square  yard.    How  much  did  the  plastering  cost? 

6.  The  carpenter  labor  amounted  to  833  §  hours  at  60  cents 
per  hour.    Find  the  total  amount  paid  the  carpenters. 

'A  perch =24|  cubic  feet. 


284  EIGHTH  YEAR 

7.  The  rear  chimney  was  35  feet  high  and  cost  $1.30  per 
linear  foot.    Compute  the  cost  of  this  chimney. 

8.  The  other  items  in  the  cost  of  the  construction  of  the 
house  were:  Lumber  $669.00;  millwork  $239.00;  hardware 
$132.00;  paint  (material  and  labor)  $190.00;  brick  for  porch 
work  $80.00;  fireplace  (chimney,  hearth,  stone,  etc.)  $105.00; 
wiring  $14.00;  and  hot-air  heating  plant  $129.00.  Find  the 
total  cost  of  these  items. 

9.  Find  the  total  cost  of  the  house  as  shown  by  the  various 
items  described  in  Problems  1  to  8  inclusive. 

10.  Find  the  total  cost  of  the  excavating,  the  foundation 
and  the  cement  floor  of  the  basement.  These  items  amounted 
to  what  per  cent  of  the  total  cost  of  the  house? 

11.  The  cost  of  the  carpenter  labor  was  what  per  cent  of  the 
total  cost  of  the  house? 

12.  The  total  cost  of  the  lumber,  millwork  and  hardware 
was  what  per  cent  of  the  cost  of  the  house? 

Exercise  3.    Furnishing  a  Home 

1.  What  size  rugs  would  you  buy  for  the  living  room  and 
the  dining  room?  What  are  the  advantages  of  rugs  over 
carpets? 

2.  Would  you  buy  rugs  for  the  two  bed  rooms?  If  so, 
what  size  would  you  buy? 

3.  How  many  shades  would  be  needed  for  the  bungalow? 

4.  Would  you  put  linoleum  on  the  kitchen  floor?  Linoleum 
is  made  in  6-ft.,  9-ft.  and  12-ft.  widths.  Which  one  of  these 
widths  would  be  used  on  the  kitchen  with  the  least  waste? 

6.  Make  out  a  list  of  the  various  articles  of  furniture  which 
you  would  buy  to  furnish  this  home  and  the  approximate  cost 
of  each  article.    Find  the  total  cost  of  these  furnishings. 


EFFICIENCY  IN  THE  HOME 


285 


6.  An  expert  in  interior  decorations  and  home  furnishings 
suggested  the  following  as  a  model  list  of  furniture  for  this 
five-room  bungalow.  Find  the  total  cost  of  furnishing  the 
bungalow  in  this  manner: 

Living  Room   (Antique  Mahogany) 

Davenport,  with  damask,  velour  or  tapestry  covering $100.00 

Chair  to  match 55 .  00 

Sofa  table  to  go  with  davenport  if  used  in  front  of  fireplace 37 .  50 

Overstuffed  arm  chair  with  velour,  tapestry  or  damask  covering . .  50 .  00 

Occasional  chair  or  rocker  in  cane  or  upholstered 18 .  50 

Sofa,  and  table  at  each  end  of  sofa,  each 12 .00 

Living  room  table,  30"X54" 45.00 

Book  case,  4'  wide 40 .  00 

Best  Grade  Wilton  Rug,  10'  6"X  13'  6" 122.00 

Dining  Room  (Tudor  Wahiut)  ^   ^^^^  l^o^  you  ^Q^ld 

^^^^ $78.00     furnish  this  house  with  an 

Serving  Table 38.00 

Extension  Table 58.00 

Cabinet 60.00 

Arm  Chair 22.00 

Side  Chairs,  5  at  $13.50 67.50 

Wilton  Rug,  11'  3"X13'0".  .110.00 
Chamber  No.  1  (American  Wahiut) 

Bed— Full  size $42.00 

Spring  and  Mattress 38 .  50 

Chest  of  Drawers 56.00 

Dresser 65 .  00 

Night  Stand 8.00 

Side  Chair  and  Side  Rocker,  ea.     9 .  00 

Wilton  Carpet,  9' XI 1' 46.00 

Chamber  No.  2  (Ivory  Enamel) 

Bed— Full  size $48.00 

Spring  and  Mattress 38. 50 

Chest  of  Drawers 36.00 

Toilet  Table 47.00 

Night  Stand 10.00 

Toilet  Table  Bench 10.00 

Side  Chair  and  Side  Rocker,  ea.  1 1 .  75 
WUtoaCarpet,  9'Xll' 46.00 


allowance  of  $800  to  cover 
all  expenses  for  furnishings. 
Get  prices  on  furniture  from 
the  local  dealer  in  making 
your  estimates. 

8.  Furnish  the  house  on 
an  allowance   of  $1000. 

9.  Which  would  be  the 
better  plan  if  your  allow- 
ance were  too  small :  to  buy 
a  full  equipment  of  cheap 
furniture  or  to  buy  fewer 
pieces  of  higher-priced  furni- 
ture? 

10.  What  articles  would 
you  provide  for  the  front 
porch?  Estimate  the  cost 
of  these  articles. 


286 


EIGHTH  YEAR 


Exercise  4 

The  house  plan  shown  in  this  illustration  is  the  one  for  the 
house  shown  on  page  121. 


1.  Compare  this  plan  with  the  plan  of  the  bungalow.    Which 
one  would  you  prefer  for  a  home?    Why? 

2.  Estimate  the  cost  of  furnishing  this  house,  listing  the 
various  articles  and  their,  prices  as  in  the  preceding  exercise. 

3.  Discuss  size  of  rugs,  number  of  windows,  etc.,  for  this 
plan  as  outlined  in  Exercise  1. 


Exercise  5.    Expenses  of  a  Home 

1.  How  many  tons  of  coal  would  be  needed  to  heat  this 
home  for  a  year?  Get  estimates  from  owners  of  houses  of  about 
the  same  size. 

2.  How  much  does  coal  cost  in  your  community?  Estimate 
the  cost  of  the  coal  at  that  price. 


EFFICIENCY  IN  THE  HOME  287 

3.  Compare  the  cost  of  burning  hard  coal  and  that  of  soft 
coal  for  a  house  of  this  size. 

4.  If  the  kitchen  range  were  a  coal  stove,  how  many  tons 
would  be  needed  to  supply  the  stove  per  year?  Find  the  cost 
of  the  coal  for  cooking  purposes  for  a  year. 

5.  If  gas  is  used  in  your  community,  find  the  cost  per  month 
for  the  average  family.    What  is  the  total  gas  bill  for  a  year? 

6.  If  estimates  for  both  coal  and  gas  can  be  obtained, 
compare  the  costs  to  see  which  is  the  more  economical. 

7.  Secure  actual  data  from  the  homes  in  your  community 
and  estimate  the  cost  of  lighting  a  home  for  a  year. 

8.  Estimate  the  table  expenses^  for  a  family  of  4  to  8  persons 
per  month? 

Campfire  Girls 

In  order  to  encourage  girls  to  become  efficient  as  home 
managers,  honors  are  granted  to  Campfire  Girls  for  the  following 
achievements : 

1.  Save  ten  per  cent  of  your  allowance  for  3  months. 

2.  Plan  the  expenditures  of  a  family  under  heads  of  shelter, 
food,  clothing,  recreation  and  miscellaneous. 

3.  Have  a  party  of  ten  with  refreshments,  costing  not  more 
than  one  dollar. 

4.  Market  for  one  week  on  $2.00  per  person. 

5.  Market  for  one  week  on  $3.00  per  person. 

6.  Give  examples  of  5  expensive  and  5  inexpensive  foods 
having  high  energy  or  tissue-forming  value.  Do  the  same  for 
foods  having  little  energy  or  tissue-forming  value. 

Choose  one  of  the  above  achievements  to  work  out  and  report 

on  it  to  the  class  at  a  later  date. 

^A  review  of  the  section  on  Food  Values  at  this  point  will  be  of  assistance 
in  planning  the  food  for  the  family  use.  A  very  elaborate  and  profitable 
treatment  can  be  made  of  this  topic. 


288 


EIGHTH  YEAR 


Exercise  6.    Keeping  the  Family  Budget 

Efficiency  in  a  business  enterprise  demands  that  the  income 
and  expenses  of  every  department  be  known.  Likewise  effi- 
ciency in  the  home  demands  that  the  home  managers  apportion 
the  family  incomes  in  the  most  advantageous  manner. 

A  large  business  corporation  made  out  a  suggestive  budget 
for  the  benefit  of  their  employees.  They  suggested  that  the 
daily  expenses  be  entered  on  an  account  sheet  similar  to  the 
following: 


Budget  Estimate  for  a  Family  of  Five 

Date 

Food 
30% 

Shelter 
20% 

Operating 

Expenses 

10% 

Clothing 
15% 

Contingency 
25% 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

etc.  to  the  c 

ose  of  each  month. 

1 

EFFICIENCY  IN  THE  HOME  289 

Under  food  they  included  meat,  groceries,  vegetables,  bakery 
and  dairy  products,  and  any  meals  at  hotels  or  restaurants. 
Shelter  included  rent  or  payments  on  owned  home,  interest  on 
mortgage,  taxes,  fire  insurance,  and  upkeep  of  the  house. 

Operating  expenses  comprise  heat,  light,  fuel  for  cooking,  ice, 
hired  help,  laundry,  telephone  and  replacement  of  home  fur- 
nishings. Contingency  includes  savings,  educational  expenses, 
church  dues,  club  dues,  concerts,  personal  expenses  and  expenses 
for  health  and  recreation. 

1.  If  the  family  income  is  $75  per  month,  find  the  amounts 
that  should  be  included  under  the  various  headings  of  the 
suggested  family  budget. 

2.  Find  the  amounts  for  family  incomes  of  $100,  $125  and 
$150  per  month. 

3.  Keep  a  family  budget  at  home  for  a  month  and  see  how 
the  amounts  expended  for  the  various  apportionments  compare 
with  the  percentage  of  the  suggested  budget. 

4.  Another  expert  on  home  economy  suggested  the  following 
classification:  Rent,  25%;  food,  25%;  clothing,  15%;  education, 
10%;  luxuries,  5%;  miscellaneous  expenses,  10%;  savings,  10%. 
Find  the  monthly  apportionments  of  this  budget  for  an  income 
of  $125. 

6.  Compare  the  apportionments  for  the  two  budgets. 
Which  is  the  most  suggestive  and  helpful  to  a  home  manager? 

6.  Bring  to  the  class  any  other  budgets  for  distributing 
the  family  income  among  various  headings  and  compare  these 
budgets  with  those  presented  in  this  chapter. 

7.  Does  the  location  (in  a  large  city,  a  small  city,  or  the 
country)  affect  the  per  cents  apportioned  among  the  various 
items  of  a  budget?    Show  why. 


290 


EIGHTH  YEAR 


EFFICIENCY  IN  BUSINESS 

The  boys  and  girls  in  the  upper  school  grades  are  the  coming 
business  men  and  women.  If  you  study  the  things  that  lead 
to  efficiency  in  business,  you  will  find  that  scientific  planning 
and  economy  in  management  are  the  essential  factors. 

The  printing  trade  is  here  used  for  illustration  only.  The 
lessons  will  apply  to  other  industries  as  well. 

Exercise  7 

Mr.  Franklin,  with  $5000  to  invest  in  the  printing  business, 
rented  floor  space  50'x28'. 

The  accompanying  diagram  will  show  how  this  space  was 
laid  out,  by  an  expert,  to  insure  the  greatest  working  convenience, 
the  'proper  proportion  of  expenditures  in  equipment  and  the 
highest  utility  of  space. 


After  a  careful  study  of  the  floor  plans,  Mr.  Franklin  pur- 
chased the  material  and  furniture  listed  on  the  following  page, 
which  it  was  found  would  give  him  a  complete  and  well-pro- 
portioned working  outfit. 


EFFICIENCY  IN  BUSINESS  291 

Wood  and  Steel  Equipment $   850.00 

Machinery,  including  Motors 1,830.00 

Type,  Spaces  and  Quads,  Borders,  Ornaments,  Brass  Rule,  Iron 

Furniture,  Quotation  Quads,  etc 1,435.00 

Miscellaneous  material  such  as  Quoins,  Mallets,  Planers,  Brushes, 
Benzine  Cans,  Ink,  Knives,  Roller  Supporters,  Composing 
Sticks,  Galleys,  and  all  the  small  tools  necessary  in  a  printing 

plant 110.00 

1  Office  Desk 55.00 

1  Counter  (built  in) 42.00 

1  Show  Case 62.00 

1  Typewriter 85.00 

4  Chairs  (average,  $7.75) 31.00 

Total 

What  balance  did  he  have  remaining  as  working  capital? 

There  was  still  another  necessary  preparation  for  the  safe 
conduct  of  the  business,  viz.,  the  establishment  of  a  cost  system 
to  include  the  overhead  charges  (see  page  74)  and  a  properly- 
classified  schedule  of  wages  for  the  three  separate  departments 
of  the  work  as  below  shown  •} 

Composing  Room  wages $0.50  per  hour 

Overhead  charges — Rent,  Heat,  Light,  etc 1.00  per  hour 

Net  cost  per  working  hour r $1.50  per  hour 

Press  Room  wages  (Gordons) 30  per  hour 

Overhead  charges — Rent,  Heat,  Light,  Power,  Insurance, 

Taxes,  etc 65  per  hour 

Net  cost  per  working  hour $0.95  per  hour 

Bindery  wages — Girls 21  per  hour 

Overhead  charges — Rent,  Heat,  Light,  Insurance,  Taxes, 

etc 24  per  hour 

Net  cost  per  working  hour $0.45  per  hour 

'The  "cost  system"  enabled  Mr.  Franklin,  at  the  end  of  each  week, 
quickly  to  determine  whether  the  business  of  each  department  was  con- 
aucted  at  a  profit,  or,  if  at  a  loss,  to  make  the  necessary  correction  and 
thus  avoid  further  risk  and  loss. 


292  EIGHTH  YEAR 

Mr.  Franklin  ordered  his  paper  from  a  wholesale  paper 
house,  by  the  ream,  in  sheets  of  various  sizes,  weights  and 
grades,  including  the  standard  lines  specified  in  the  second 
column  of  the  problems  below. 

Let  us  now  find  the  largest  number  of  circulars  5"x7"  that 
can  be  cut  from  a  sheet  21''x36"K 

Solution:  3      7 

21x30 

=  21 

0x7 

Note  that  5  is  canceled  into  36,  7-  times,  the  fraction  being  discarded. 

Show  the  amount  of  waste  in  square  inches. 

Find  the  number  of  circulars,  or  pieces  of  paper  of  the  sizes 
given  in  the  first  column,  that  can  be  cut  with  the  least  waste 
from  the  sizes  given  in  the  second  column,  and  show  the  amount 
of  waste  for  each  in  square  inches. 


1. 

8|'xir 

from 

17' X  22' 

6.  6|'  X   9' 

from 

26' X  29' 

2. 

4'    X   5i' 

from 

22' X  28' 

7.  7'    X  10' 

from 

28' X  42' 

3. 

Si'xW 

from 

22' X  34' 

8.  8'    X 10^' 

from 

32' X  44' 

4. 

4|'x   8' 

from 

24' X  36' 

9.  9'    X  11' 

from 

35' X  45' 

5. 

6|'x   9' 

from 

25' X  38' 

10.  9'    X  12' 

from 

38' X  50* 

Exercise  8 

1.  For  a  certain  job  of  printing,  2  reams  of  book  paper 

were  needed,  weighing  80  pounds  to  the  ream,  and  costing 

8  cents  per  pound.    The  composition  (type  setting)  required 

8  hours,  the  press  work  6  hours  and  the  bindery  work  3  hours. 

What  was  the  net  cost  based  on  the  "working  hour"  rates 

given  in  the  table  on  page  303? 

^In  arriving  at  the  amount  of  paper  required  for  a  job,  printers  by  the 
use  of  cancellation  are  able  to  see  at  a  glance  the  sized  sheet  they  may 
have  in  stock  from  which  they  can  cut  with  the  least  waste. 


EFFICIENCY  IN  BUSINESS  293 

2.  If  the  printing  office  added  20%  for  profit,  what  was  the 
total  cost  of  the  job  to  the  customer? 

3.  Mr.  Howe,  a  merchant,  ordered  6000  handbills,  size 
6j"x9",  for  his  anniversary  dry  goods  sale.  How  many  reams 
of  paper  were  required  for  this  job  if  cut  from  sheets  25"x38"? 

4.  If  the  paper  cost  6  cents  per  pound  and  weighed 
60  pounds  to  the  ream,  what  did  the  paper  cost? 

6  If  the  composition  required  l|-  hours  and  the  press  work 
2  hours,  what  was  the  cost  of  these  two  items  at  the  net  prices 
given  in  the  table? 

6.  If  Mr.  Franklin  added  20%  for  his  margin  of  profit  on 
the  job,  what  did  the  6000  handbills  cost  Mr.  Howe? 

7.  A  High  School  Glee  Club  ordered  500  programs  for  their 
annual  entertainment,  size  (before  folding)  6 j''x9",  printed  on 
both  sides  from  stock  weighing  100  pounds  to  the  ream.  How 
many  sheets  25"x38"  were  required,  and  what  was  the  cost  of 
the  paper  at  10  cents  per  pound? 

8.  If  the  composition  required  5  hours  and  the  press  work 
4  hours,  what  was  the  charge  to  the  Glee  Club,  counting  in  the 
office  charge  of  20%? 

9.  A  graduating  class  ordered  1500  programs,  size  4"x6". 
What  paper  size  given  in  the  table  cut  to  the  best  advantage, 
and  how  many  sheets  were  required? 

10.  A  School  Board  ordered  2000  letterheads,  size  Sj^'xll". 
If  these  were  cut  from  sheets  17''x22",  of  paper  stock  costing 
9  cents  per  pound,  and  weighing  90  pounds  to  the  ream,  the 
composition  requiring  1  hour,  and  the  press  work  2  hours,  and 
20%  was  added  for  profit,  what  was  the  total  charge  for  the  job? 

11.  Find  some  printed  program,  estimate  its  cost  based  on 
the  tables  given,  submit  your  figures  to  your  local  printer,  and 
see  how  near  you  have  reached  the  correct  amount. 


CHAPTER  VI 

PRACTICAL  MEASURING  INSTRUMENTS 

The  Thermometer 

The  Fahrenheit  thermometer  is  the  standard 
measure  of  temperature  in  the  United  States. 

A  thermometer  consists  of  a  small  glass  tube 
ending  in  either  a  spherical  or  a  cylindrical  bulb. 
At  the  temperature  of  your  room,  the  bulb  and 
part  of  the  tube  is  filled  with  a  liquid  (usually 
mercury). 

Hold  the  bulb  of  a  thermometer  at  your  mouth 
and  slowly  blow  on  it.  What  happens  to  the 
mercury?  The  heat  from  your  mouth  has  caused 
the  mercury  to  expand.  Hold  the  bulb  for  a 
few  moments  in  some  cold  water.  What  change 
has  taken  place  in  the  column  of  mercury  in 
the  tube? 

The  thermometer  can  thus  be  used  to  measure 
the  temperature  of  the  air  and  certain  liquids. 
There  are  two  important  points  on  a  Fahrenheit 
thermometer:  the  freezing  point  of  water,  which 
is  marked  32°  above  zero,  and  the  boiling  point 
of  water,  which  is  marked  212°  above  zero. 
Most  scientists  use  the  Centigrade  thermometer,  which  has 
the  freezing  point  marked  0°  and  the  boiling  point  marked  100°. 


A  Standard 
Thermometer 


Exercise  1 
1.  Find  from  a  physics  book  or  the  encyclopedia  how  a 
thermometer  is  made.    Explain  to  the  class  how  the  freezing 
and  boiling  points  are  found. 


294 


PRACTICAL  MEASURING  INSTRUMENTS     295 

2.  How  many  degrees  are  there  between  the  freezing  and 
boiUng  points  on  a  Fahrenheit  thermometer? 

In  order  that  temperatures  above  and  below  zero  may  be 
distinguished,  the  signs  +  and  —  are  usually  used;  +20° 
meaning  20°  above  zero  and  —20°  meaning  20°  below  zero. 

3.  What  is  the  difference  in  degrees  between  a  temperature 
of  +20°  and  a  temperature  of  -20°? 

4.  At  a  certain  city  the  temperature  on  a  certain  day  at 
noon  was  25°.  At  midnight  of  the  following  day  the  tempera- 
ture was  —4°.    How  many  degrees  had  the  temperature  fallen? 

Give  the  changes  in  the  temperature  indicated  by  the  follow- 
ing readings: 

6.  +50°  to +32°  9.  -  5°  to +10°  13.  +40°    to +101° 

6.  +15°  to-  2°  10.  +32°  to +98  J°  14.  -  1°    to  -  16° 

7.  +77°  to +92°  11.  +  2°  to +36°  16.  -15°    to  +  15° 

8.  +60° to +43°  12.  -20° to +32°  16.  +98|°to +10l|° 

At  government  observatories,  the  temperature  is  taken  each 
hour.  The  following  extract  from  a  daily  paper  shows  a  portion 
of  the  weather  record  in  a  certain  city  on  Feb.  9,  1917: 

12  midnight 4  7  a.  m — 1 

1  a.  m 3  8  a.  m — 2 

2  a.  m 2  9  a.  m 0 

3  a.  m 1  10  a.  m 2 

4  a.  m 0  11  a.  m 4 

5  a.  m — 1  12  noon 4 

6  a.  m — 1 

17.  What  was  the  maximum,  or  highest,  temperature  during 
the  time  indicated? 

18.  What  was  the  minimum,  or  lowest,  temperature? 

19.  What  was  the  range  or  change  in  temperature  during 
the  12  hours  indicated? 


296 


EIGHTH  YEAR 


20.  Keep  a  daily  record  of  the  outside  temperature  at  the 
school  house.  Leave  this  for  the  pupils  of  next  year's  class. 
They  will  be  able  to  make  some  interesting  comparisons  with 
the  record  that  they  are  keeping. 


The  Barometer 

A  barometer  is  an  instrument  to  measure  the 
pressure  of  the  air. 

A  simple  barometer  may  be  made  by  inverting 
a  tube,  filled  with  mercury,  in  a  dish  of  mercury. 
If  the  tube  is  longer  than  30  inches,  the  mercury  will 
drop  from  the  end  of  the  tube,  leaving  a  vacuum 
above  it.  The  pressure  of  the  air  on  the  surface 
of  the  mercury  in  the  dish  will  support  a  column  of 
mercury  30  inches  high  at  sea  level.  If  one  goes  up 
in  a  balloon  or  climbs  a  mountain,  the  column  of 
mercury  in  the  tube  will  gradually  fall  because 
the  higher  above  sea  level  one  rises  the  less  air  there 
is  to  press  down. 

The  barometer  is  a  very  important  instrument 
in  predicting  weather  conditions.  When  the 
barometer   is   very   low,    stormy   weather    usually 

A  Standard  results,  and  when  the  barometer  is  extremely  high, 

Barometer    fair  weather  usually  results. 

Exercise  2 

1.  Suppose  the  barometer  tube  has  an  area  of  1  square 
inch  at  the  base,  and  the  air  supports  a  column  of  mercury 
30  inches  high.  How  much  is  the  pressure  of  the  air  per  square 
inch,  if  mercury  weighs  .49  pound  per  cubic  inch? 

Solution:  A  column  of  mercury  1  square  inch  at  the  base  and  30  inches 
high  contains  30  cubic  inches.  30 X. 49  pounds  =  14.7  pounds.  Since  the 
column  of  mercury  weighs  14.7  pounds,  the  air  pressure  must  be  14.7 
pounds  on  each  square  inch  of  surface. 


PRACTICAL  MEASURING  INSTRUMENTS      297 

2.  Find  the  number  of  square  inches  on  the  top  of  your 
desk.  How  much  pressure  does  the  air  exert  on  the  top  of  this 
desk? 

3.  The  area  of  an  average  person's  body  is  30  square  feet. 
Find  the  total  pressure  which  the  air  is  exerting  on  our  bodies. 

Our  bodies  are  built  to  withstand  this  enormous  pressure. 
If  we  go  up  a  high  mountain,  the  outside  pressure  becomes  so 
much  less  that  the  pressure  of  the  blood  is  apt  to  break  the 
blood  vessels,  and  bleeding  at  the  nose  and  ears  often  results. 


The  Hygrometer 


It  is  important  not  only  to  know  whether  the 
air  is  light  or  heavy  as  shown  by  the  barometer, 
but  also  to  know  how  much  moisture  it  contains. 
The  instrument  for  measuring  the  amount  of 
moisture  in  the  air  is  called  a  hygrometer. 

One  of  the  common  forms  of  hygrometers  is  the 
wet  and  dry  bulb  type.  One  of  the  thermometers 
is  an  ordinary  thermometer;  the  other  thermom- 
eter has  its  bulb  covered  with  a  wick  which  is 
dipping  in  a  can  of  water.  Evaporation  of  any  liquid  has 
a  cooling  effect.  Drop  some  gasoline  on  the  back  of  your 
hand  and  see  how  cool  it  feels  when  it  is  evaporating  into  the 
air.  If  there  is  a  very  little  moisture  in  the  air,  the  water  will 
evaporate  rapidly  from  the  wick  and  cool  it.  The  wet  ther- 
mometer will  then  read  lower  than  the  dry  thermometer. 

If  there  is  a  great  deal  of  moisture  in  the  air,  the  evaporation 
will  not  be  so  rapid  and  the  difference  in  the  readings  of  the  two 
thermometers  will  not  be  so  great.  By  the  use  of  tables  pre- 
pared for  this  hygrometer,  the  amount  of  moisture  in  the  air 
can  be  found. 

The  amount  of  moisture  in  the  air  is  expressed  in  terms  of  its 
relative  humidity.    If  we  say  that  the  relative  humidity  of  the 


298 


EIGHTH  YEAR 


air  is  65%,  that  means  that  the  air  now  contains  65%  as  much 
moisture  as  it  is  capable  of  holding.  The  relative  humidity 
of  a  living  room  should  be  between  50%  and  65%.  If  the  air 
gets  too  dry,  moisture  will  evaporate  too  rapidly  from  the 
body  and  chill  the  skin.  The  pores  of  the  skin  will  then  be 
closed,  preventing  the  elimination  of  certain  waste  products 
through  the  glands  of  the  skin.  If  the  air  of  a  room  is  too  dry, 
an  open  vessel  containing  water  should  be  placed  on  the  stove 
or  radiator  to  supply  the  necessary  moisture. 


WEATHER  REPORTS 


WEATHER  FORECAST 


AN  ANEROID 
BAROMETER" 


For  City  and  vicinity — 

Partly  cloudy  Wednes- 
day    and     Thursday, 

probably    local    thun- 

dershowers,  continued 

warm  Wednesday;  not 

so    warm     Thursday; 

fresh  southerly  winds 

Wednesday,  becoming 

variable  Thursday. 
For  Central  territory — 

Partly    cloudy     Wed- 
nesday and  Thursday, 

probably    local    thun- 

dershowers;      not      so 

warm  Thursday  in  the 

northern  portion;  moderate,  eouthwest  winds. 
Sunrise,  4:19;  sunset,  7:14;  moonset,  10:17  p.  m. 


TEMPERATURE 

During    24    hours 


Maximum,  2  p.  m 93 

Minimum,  6  a.  m 75 


3  a.  m. 

4  a.  m. 
£  a.  m. 

6  a.  m. 

7  a.  m. 

8  a.  m. 

9  a.  m. 
10  a.  m. 


11  a.  m 85 

Noon 88 


1  p.  m. 

2  p.  m. 

3  p.  m. 

4  p.  m. 

5  p.  m. 

6  p.  m. 


.  7  p.  m 88 

8  p.  m 85 

9  p.  m 84 

10  p.  m...80.5 

11  p.  m 80 

Midnight...  79 

1  a.  m 79 

2  a.  m 78 


Mean  temperature,  83.5;  normal  for       the  day,60 

Excess  since  Jan.  1,  363. 
Precipitation  for  24  hours  to  7  p.  m.,  U.    Defieiency 

since  Jan.  1,  2.17  inche.s. 
Wind,  S.  W.;  max.,  24  miles  an  hour,  at  8:35  a.  m. 
Relative  humidity,  7  a    m.,  67%;  7  p.  m.,  52%. 
Barometer,  sea  level,  7.  a.  m.,  30.02;  7  p.  m..  SO.Oli 
A  Daily  Paper's  Weather  Record. 


One  of  the  most 
beneficial  depart- 
ments  of  our  govern- 
ment is  the  weather 
bureau.  By  means 
of  observations  taken 
in  various  cities  scat- 
tered all  over  the 
country,  weather  fore- 
casts can  be  made 
which  save  farmers 
and  shippers  thou- 
sands of  dollars. 

The  weather  record 
of  the  preceding  day 
is  shown  at  the  left 
as  it  appeared  on  a 
certain  day  in  a  large 
daily  paper.  We  have 
now  studied  some  of 
the  instruments  which 
are  used  in  making 
these  observations. 


PRACTICAL  MEASURING  INSTRUMENTS      299 

Exercise  3 

By  reference  to  the  above  record  answer  the  following  ques- 
tions: 

1.  What  was  the  mean  temperature  for  the  day? 

2.  Was  this  temperature  warmer  or  cooler  than  is  usually 
observed  on  this  particular  day  of  the  year? 

3.  What  was  the  difference  between  the  maximum  and 
the  minimum  temperature  for  the  day? 

4.  Has  the  weather  during  this  year  since  Jan.  1  been 
warmer  or  cooler  than  the  average  year's  temperature? 

6.  Did  any  rain  fall  during  the  day?  Has  as  much  rain 
fallen  during  this  year  since  Jan.  1  as  is  usually  observed? 

(The  amount  of  rainfall  is  measured  each  day  by  the  amoimt  of  water 
falling  in  an  open  vessel  with  perpendicular  sides.) 

6.  From  what  direction  was  the  wind  blowing?  What 
was  its  velocity? 

(The  velocity  of  the  wind  is  measured  by  an  instrument  called  an 
anemometer,  which  may  be  described  as  a  cup-shaped  windmill  so  arranged 
that  it  shows  the  velocity  of  the  wind  by  the  rapidity  with  which  the 
wind  makes  it  revolve.) 

7.  What  was  the  relative  humidity  of  the  air  at  7  a.  m.? 
At  7  p.  m.?    Explain  what  is  meant  by  relative  humidity'/ 

8.  What  was  the  change  in  the  pressure  of  the  air,  as 
measured  by  the  barometer,  between  7  a.  m.  and  7  p.  m.? 

9.  From  the  preceding  observations  and  other  similar 
ones  made  in  other  cities  scattered  over  the  country,  the  weather 
forecaster  makes  predictions  on  what  the  weather  will  be. 
What  was  his  forecast? 

10.  Bring  in  other  daily  records  clipped  from  your  daily 
papers  and  compare  the  records  and  forecasts  with  this  one. 


300  EIGHTH  YEAR 

Uses  of  Weather  Reports 

By  taking  observations  over  this  country  and  Canada, 
forecasters  are  able  to  warn  farmers  and  shippers  of  storms 
and  cold  waves.  Rain  storms  usually  sweep  over  the  country 
from  the  southwest  to  the  northeast,  taking  several  days  to 
travel  across  the  country.  Farmers  can  thus  be  warned  of 
an  approaching  storm  and  make  their  plans  accordingly. 

Shippers  pack  perishable  produce  in  cars  to  withstand  certain 
temperatures.  If  a  cold  wave  is  approaching,  they  must  pack 
their  cars  to  withstand  the  lower  temperature.  In  the  summer, 
more  ice  must  be  put  in  the  refrigerator  cars  if  a  hot  wave  is 
approaching.  The  government  issues  bulletins  to  shippers 
telling  them  what  temperatures  they  may  expect. 

Exercise  4 

1.  A  farmer  had,  in  process  of  curing,  five  acres  of  new  mown 
hay.  Counting  on  fair  weather  and  failing  to  profit  by  his 
daily  paper's  "Weather  Forecast,"  he  had  his  crop  damaged  to 
the  extent  of  35%  during  an  unexpected  rainstorm.  How 
much  did  he  lose,  on  11  tons  of  hay,  counting  the  full  market 
value  at  $11.40  per  ton? 

2.  In  a  certain  fruit  belt  the  temperature  dropped  unex- 
pectedly, over  night,  from  51  degrees  to  30  degrees  above  zero. 
The  peach  crop  that  year  in  a  certain  locality  yielded  3768 
baskets.  In  the  season  following,  under  normal  conditions, 
the  yield  was  7348  baskets.  What  was  this  increased  product 
worth  at  55ff  per  basket? 

3.  In  some  localities  the  temperature  of  the  air  is  kept 
higher  by  building  fires  all  over  an  orchard.  If  the  fruit  growers 
in  the  locaUty  described  in  the  preceding  problem  had  heeded 
the  warning  issued  by  the  govermnent  and  built  suitable  fires, 
how  much  loss  might  they  have  prevented? 


PRACTICAL  MEASURING  INSTRUMENTS      301 

4.  A  farmer  observed  that  the  weather  report  said:  "Con- 
tinued dry  weather  may  be  expected."  He  dragged  an  old 
mower  wheel  between  the  rows  of  his  corn,  thus  forming  a  mulch 
and  conserving  the  moisture  in  the  ground  by  preventing  its 
evaporation.  His  yield  was  40  bushels  per  acre.  Another 
farmer  who  paid  no  attention  to  the  reports  of  the  weather 
bureau  and  knew  nothing  of  dry  farming  methods  plowed  his 
corn  deep  and  his  ground  dried  out  so  that  his  yield  was  only 
25  bushels  per  acre.  If  both  farmers  had  equally  good  land 
and  prospects  for  corn,  how  much  did  the  first  farmer  make 
per  acre  by  dragging  his  corn,  if  it  sold  for  75)!l  per  bushel? 

5.  The  precipitation  in  a  certain  township  in  one  season 
was  26.8  inches.  The  wheat  yield  that  year  in  the  township 
aggregated  137,540  bushels.  In  the  succeeding  year  the  pre- 
cipitation during  the  same  period  was  19.7  inches,  and  the 
wheat  yield  aggregated  68,430  bushels.  What  was  the  differ- 
ence in  the  value  of  the  crops  at  95^  per  bushel? 

6.  A  gallon  contains  231  cubic  inches.  An  acre  of  ground 
contains  43,560  square  feet.  What  would  be  the  weight,  in 
tons,  of  a  rainfall  of  one  inch  in  depth  over  a  quarter-section  of 
land,  estimating  the  weight  of  each  gallon  of  water  at  8^ 
pounds? 

7.  A  fruit  grower  in  Georgia  shipped  a  carload  of  peaches 
which  were  damaged  by  a  hot  wave  striking  the  country  while 
the  car  was  on  the  way.  Having  insufficient  ice  to  withstand 
the  hot  wave,  the  peaches  were  damaged  25  f^  per  bushel.  If 
the  car  contained  420  bushels  of  peaches,  what  was  the  shipper's 
loss  due  to  the  change  of  weather?  He  might  have  prevented 
this  loss  if  he  had  heeded  the  government's  warning. 

8.  Tell  of  any  instances  in  which  you  have  heard  of  farmers 
or  fruit  growers  profiting  by  the  weather  reports  in  the  news- 
papers. 

9.  Bring  to  class  newspapers  containing  weather  reports. 


302 


EIGHTH  YEAR 


THE  ELECTRIC  METER 

If  we  burn  coal  under  a  boiler,  we  generate  steam.  This 
steam  may  be  used  to  run  a  steam  engine  which  in  turn  may 
run  a  dynamo  which  generates  an  electrical  current.  This 
electric  current  supplies  the  power  for  electric  lights,  electric 
motors  and  runs  our  street  cars  and  interurban  lines. 

Steam  engines  and  gas  engines  are  generally  rated  by  the 
horse  power  in  this  country.  We  say  the  engine  in  an  automo- 
bile is  40  horse  power  or  60  horse  power. 

Electric  energy  is  measured  in  terms  of  kilowatts.  A  kilowatt 
is  equal  to  1^  horse  power.  Thus  an  engine  rated  at  40  horse 
power  would  be  rated  at  30  kilowatts. 

Electric  light  companies  generally  measure  the  current  you 
use  in  terms  of  kilowatt-hours.  A  kilowatt-hour  is  equal  to 
the  use  of  1  kilowatt  of  energy  for  1  hour.  For  clearness  we 
may  say  that  a  kilowatt-hour  is  equal  to  the  energy  which  a 
good  horse  would  supply  in  working  steadily  for  1^  hours. 
Electric  meters  are  instruments  used  to  measure  the  amount  of 
electrical  energy  which  we  use. 


How  to  Read  an  Electric  Meter 

Beginning  at  the  left 
indicator  on  the  dial  we  see 
that  the  reading  is  some- 
where between  2000  and 
3000  because  over  this  dial 
we  see  that  these  figures  are 
read  in  thousands.  Going  to  the  right  we  see  hundreds,  tens, 
ones,  and  tenths  dials.  We  can  easily  read  such  a  dial  because 
it  is  just  like  writing  numbers  with  figures  in  thousands,  hun- 
dreds, tens,  units  and  tenths.  As  we  read  the  dial  we  take  the 
figure  that  the  dial  is  at  or  has  just  passed.  The  reading  is 
2438  kilowatt-hours. 


PRACTICAL  MEASURING  INSTRUMENTS      303 


Kilowatt  -  Hours 


The  dial  at  the  right  is  the 
same  as  the  preceding  dial 
except  that  the  tenths  indi- 
cator is  absent. 

Some  meters  have  differ- 
ent dials  on  them.     If  the 

dial  on  your  meter  at  school  or  at  home  is  different,  work  out 
the  method  of  reading  it  and  then  check  your  result  by  the 
reading  on  the  light  bill.  If  you  can  not  read  it,  have  the  officer 
of  the  company,  who  calls  each  month  to  get  the  reading, 
explain  how  it  is  read. 

Exercise  5 

1.  What  is  the  reading  on  the  dial  with  4  indicators  on  it? 

2.  The  reading  of  the  meter  of  Problem  1,  for  the  previous 
month,  was  1782.  How  many  kilowatts  has  the  family  used 
during  the  past  month? 

3.  If  the  local  rate  is  12^j^  per  kilowatt,  what  was  the  light 
bill  for  last  month? 

4.  Many  light  companies  have  a  sliding  scale  for  the  use  of 
electrical  energy. 

The  following  shows  a  bill  of  a  company  which  generates  its  energy  by 
water  power.     Note  the  low  rates  for  energy  from  water  power. 
Meter  Readings  Dec.  13. . . .  2416 
Nov.  13. . . .  2368 
Total  consumption  in  k.w.hrs. 


48 


Date: 


First     9  k.w.  hrs.  ( 

Second  9  k.w.  hrs.  ( 

30  k.  w.  hrs.  excess 

over  18  ( 

Gross  Bill 


10c =  $0.90 
6c=       .54 


3c  = 


.90 


Dec.  22,  1916. 

Discount  on  first  18  hrs.  if  paid  on 

or  before  Jan.  1,  @  Ic  per  k.  w. 


$2.34 


.18 


NetBiU  $2.16 

5.  The   reading   on  Jan.    13   of   the   meter  described  in 

Problem  4  was  2458.    (Problem  4  gives  the  reading  for  Dec.  13.) 

Figure  out  the  bill  for  this  month  according  to  the  plan  shown 

in  Problem  4. 


304  EIGHTH  YEAR 

6.  A  company  in  a  small  village  charges  ISjif  per  kilowatt 
hour  for  their  electrical  energy.  How  much  will  a  family  pay 
which  uses  16  kilowatts  during  a  certain  month? 

7.  Draw  a  diagram,  similar  to  the  one  shown  in  the  book, 
of  the  dial  of  some  electric  meter  which  is  convenient  for  you 
to  read.  What  is  the  reading  of  the  meter  shown  by  your 
diagram? 

8.  Determine  the  system  of  computing  charges  for  your 
community.  Get  some  actual  readings  from  bills  in  your 
community  and  make  a  problem.  Present  it  to  the  class  for 
solution. 

9.  Electric  cars  are  run  by  storage  batteries.  They  can  be 
charged  by  running  an  electric  current  through  them.  After 
they  are  disconnected  from  the  charging  current  they  will 
give  back  the  energy  stored  up  on  their  plates.  Find  the  cost 
of  charging  a  storage  battery.  How  many  miles  will  this 
battery  run  the  car  in  which  it  is  used?  Find  the  cost  per  mile 
for  the  current  necessary  to  run  this  electric  car. 

10.  Find  the  number  of  miles  a  gallon  of  gasoline  will  run 
an  automobile  of  about  the  same  weight.  Find  the  cost  per 
mile  of  the  gasoline.  Compare  this  cost  per  mile  with  that  of 
the  electric  car. 

THE  GAS  METER 

Illuminating  gas  is  made  from  soft  coal  by  driving  off  the  volatile  gases 
by  means  of  fires  under  closed  retorts.  This  gas  is  then  run  through 
several  processes  to  take  out  the  impurities  which  are  driven  off  with  the 
gas.  The  purified  illuminating  gas  is  then  pumped  into  large  tanks  where 
it  is  kept  under  a  pressure  which  forces  it  through  the  pipes  to  the  con- 
sumers. 

The  consumption  of  illuminating  gas  is  measured  in  terms  of 
cubic  feet.  The  gas  meter  records  the  number  of  thousand 
cubic  feet  used.     The  indicators  on  the  dial  at  the  left  are 


PRACTICAL  MEASURING  INSTRUMENTS      305 


labeled  100  thousand,  10 
thousand  and  1  thousand. 
They  really  read  in  10 
thousands,  thousands  and 
hundreds.  Hence  the  cor- 
rect reading  is  only  one- 
tenth  the  reading  as  indi- 
cated on  the  dial. 


Cubic   {^•^)  Feet 


s^^^W%^o552^   SS^5^ 


The  reading  on  the  dial  at 
the  right  as  above  corrected  is  87,300. 


Exercise  6 

1.  The  reading  on  my  gas  meter  on  Oct.  27  was  83,800. 
On  Nov.  27  it  was  85,600.  What  was  my  gas  bill  for  the 
month,  gas  selling  at  90jii  per  1000  cubic  feet? 


Solution: 


Nov.  27 
Oct.  27 


85600 
83800 


1800    number  of  cubic  feet  consumed. 
1800  cubic  feet  at  90)4  per  thousand  =  1.8X90i«  =$1.62  (gross  bill.) 

2.  If  I  am  allowed  a  discount  on  this  bill  of  lOji  per  1000 
cubic  feet  if  I  pay  it  within  10  days,  what  is  my  net  bill? 

3.  Problem  1  gives  the  reading  for  Nov.  27.  If  my  reading 
for  Dec.  27  is  87,400,  what  is  my  gas  bill  for  the  month  of  Dec? 

(Find  both  gross  and  net  bill,  using  the  same  rates  as  given 
in  Problems  1  and  2.) 

4.  If  I  use  2400  cubic  feet  of  gas  during  the  month  of  July, 
what  is  my  gas  bill  at  90^  per  thousand  cubic  feet  and  lOji  per 
thousand  cubic  feet  discount  if  paid  within  10  days? 

6.  If  you  live  in  a  city  where  gas  is  used,  find  the  cost  per 
thousand  cubic  feet.    Is  there  a  discount  for  prompt  payment? 


306  EIGHTH  YEAR 

6.  Get  an  old  gas  bill  and  make  a  problem  similar  to  the 
ones  given  above  and  present  it  to  the  class  for  solution.  Check 
their  solution  by  the  amount  as  stated  on  the  bill. 

THE  STEAM  GAUGE 

The  steam  gauge  is  an  instrument  to 
measure  the  pressure  of  the  steam  in  a 
boiler.  These  gauges  can  also  be  used  to 
indicate  the  pressure  of  compressed  air  in 
tanks.  They  are  usually  graduated  to 
read  pressure  in  so  many  pounds  to  the 
square  inch.  The  gauge  shown  in  the 
illustration  shows  no  pressure,  the  pointer  standing  at  zero. 

Exercise  7 

1.  How  many  pounds  of  pressure  must  be  put  in  an  auto- 
mobile tire  to  make  it  sufficiently  hard? 

2.  A  safety  valve  is  placed  in  a  boiler  so  that  the  pressure 
will  not  become  too  great  and  explode  the  boiler.  Ask  the 
janitor  of  your  school  building  how  many  pounds  of  steam  his 
boiler  will  carry  before  the  steam  forces  its  way  out  of  the 
safety  valve. 

3.  Most  steam  heating  plants  have  low  pressure  boilers. 
Locomotives  and  engines  have  high  pressure  boilers.  Ask  an 
engineer  how  many  pounds  he  aims  to  carry  on  his  engine. 

4.  The  pressure  of  the  atmosphere  is  about  14.7  pounds  per 
square  inch.  The  steam  gauge  reads  additional  pressure  above 
the  pressure  of  the  air.  For  example,  if  a  steam  gauge  reads 
14.7  pounds,  we  say  the  boiler  is  under  two  atmospheres  of 
pressure  inside  and  only  one  atmosphere  of  pressure  on  the 
outside.  If  the  gauge  reads  29.4  pounds,  what  would  be  the 
pressure  on  the  inside  and  outside? 


PRACTICAL  MEASURING  INSTRUMENTS     "307 

MEASUREMENTS  OF  THE  EARTH'S  SURFACE 

Short  distances  on  land  are  measured 
by  means  of  the  surveyor's  chain,  which 
is  sixty-six  feet  long  and  has  one  hundred 

links.  Surveyor's  Chain 

Distances  on  the  water,  and  long  distances  by  land,  are 
measured  by  observing  the  sun  and  other  heavenly  bodies, 
which  seem  to  pass  over  the  heavens  and  entirely  around  the 
world  in  twenty-four  hours. 

Distance  east  and  west  measured  in  this  way  is  callea  longi- 
tude. This  old  word  meant  length;  and  the  ancient  peoples 
who  lived  on  the  shores  of  the  "long-east-and-west"  Mediter- 
ranean Sea  supposed  that  the  length  of  the  world  was  east  and 
west.  They  did  not  know  that  the  world  is  round  and  they 
gave  us  the  word  longitude. 

It  is  customary  to  measure  longitude  from  some  great 
observatory,  where  the  heavenly  bodies  are  observed  through 
the  best  instruments.  Since  the  one  at  Greenwich  (grin  nij) 
near  London,  England,  is  the  best  known  in  the  world,  longitude 
is  generally  reckoned  from  that  one. 

To  make  the  distances  east  and  west,  imaginary  lines  are 
drawn  north  and  south  from  the  North 
Pole  to  the  South  Pole.  These  imaginary 
lines  are  called  meridians.  All  places 
between  the  poles  along  the  same  meridian 
have  the  same  longitude. 

The  Equator,  which  crosses  every  merid- 
ian at  right  angles  half-way  between  the 
poles,  is  the  line  from  which  distance  is  measured  in  degrees 
north  and  south.  Imaginary  circles  to  indicate  latitude,  or 
distance  north  or  south  from  the  Equator,  are  called  parallels 
of  latitude. 


308 


EIGHTH  YEAR 
THE  MEASUREMENT  OF  TIME 


tNVCH 


Suppose  it  is  noon  at  the  place  where  you  live  and  the  sun 
is  directly  south  of  you.  As  the  earth  rotates  from  west  to 
east,  the  sun  seems  to  move  westward  and  noon  travels  with 
the  sun.  Since  the  earth  rotates  on  its  axis  once  in  24  hours, 
the  sun  will  seem  to  pass  over  360°  of  longitude  in  24  hours, 
or  15°  of  longitude  in  1  hour. 

Exercise  8 

1.  If  it  is  noon  where  you  live,  how  long  will  it  be  before 
it  is  noon  15°  west  of  you?    30°  west  of  you?    45°  west  of  you? 

2.  What  time  is  it  15°  west  of  you?  30°  west  of  you? 
45°  west  of  you? 

3.  How  long  has  it  been  since  the  sun  was  directly  over 
the  meridian  15°  east  of  you?  What  time  is  it  at  a  place  15° 
east  of  you?    What  time  is  it  30°  east  of  you? 

For  convenience,  time  must  be  reckoned  from  a  certain 
meridian.  This  meridian  has  been  chosen  as  that  of  Greenwich, 
England.  All  longitude  west  of  this  meridian  to  the  180th  is 
called  west  longitude  and  all  longitude  east  of  this  meridian  to 
the  180th  is  called  east  longitude. 


STANDARD  TIME 


309 


4.  If  it  is  noon  at  Greenwich,  what  time  will  it  be  15°  west 
of  Greenwich?    30°  west  of  Greenwich? 

5.  If  I  set  my  watch  at  Greenwich  and  carry  it  west  with 
me  to  longitude  90°  west  without  re-setting  it,  how  much  too 
fast  will  it  be? 

6.  Philadelphia  is  in  about  75°  west  longitude.  When  it 
is  noon  at  Greenwich,  what  time  is  it  in  Philadelphia? 

7.  Since  there  are  about  60°  of  longitude  between  the 
extreme  east  and  west  coasts  of  the  United  States,  what  is 
the  difference  in  time  between  a  city  in  Maine  and  a  city  in 
western  Oregon? 


Standard  Time 

All  places  on  the  same  degree  of  longitude  have  the  same 
local  time,  however  far  apart  they  may  be  north  and  south; 
but  by  far  the  greater  amount  of  travel  in  the  world  is  in  an 
easterly  or  westerly  direction,  and  to  one  traveling  east  or 
west  the  local  time  changes  constantly.    It  is  especially  impor- 


310  EIGHTH  YEAR 

tant  that  railways  shall  have  an  unvarying  standard  of  time 
for  long  distances.  Hence  a  system  of  Standard  Time  has 
been  adopted  for  this  great  country,  by  which  its  area  has 
been  divided  into  four  great  time  sections,  known  as  the  Divi- 
sions of  Eastern  Time,  Central  Time,  Mountain  Time  and 
Pacific  Time. 

At  all  points  in  any  one  of  these  Divisions,  the  time  is  made 
artificially  the  same.  When  it  is  noon  in  the  Eastern  Division, 
it  is  11  o'clock  in  the  Central  Division,  10  o'clock  in  the  Moun- 
tain Division  and  9  o'clock  in  the  Pacific  Division.  Thus 
the  Divisions  are,  successively,  one  hour  apart. 

When  travelers  going  east  or  west  arrive  at  the  boundary 
line  of  one  of  these  divisions,  they  set  their  watches  ahead  or 
back,  to  correspond  with  the  time  in  the  next  division.  The 
Southern  Pacific  Railway  makes  no  use  of  Mountain  Time, 
but  passes  directly  through  from  Pacific  Time  to  Central  Time. 

It  will  be  noted  that  the  Maritime  Provinces  of  the  Dominion 
of  Canada  make  use  of  what  is  called  Atlantic  Time,  which  is 
the  time  of  the  meridian  of  Long.  60°  W.  This  time  is  not 
employed  in  the  United  States. 

Exercise  9 

1.  When  it  is  12:15  a.  m.  at  Chicago,  what  time  is  it  in 
New  York  (Standard  Tune)? 

2.  When  it  is  4:32  p.  m.  at  San  Francisco,  what  time  is  it 
in  Chicago? 

3.  When  it  is  9:45  at  New  York,  what  time  is  it  at 
Denver? 

4.  Detroit  is  now  under  Eastern  Time.  How  much  differ- 
ence is  there  between  the  time  in  Detroit  and  the  time  at 
Cincinnati,  which  is  in  the  Central  Time  belt  but  has  practically 
the  same  longitude? 


INTERNATIONAL  DATE  LINE 


311 


6.  Buffalo,  being  at  the  line  of  division  between  Eastern 
Time  and  Central  Time,  makes  use  of  both.  How  far  apart 
are  clocks  and  watches  found  to  be  in  a  city  so  situated?  Men- 
tion some  other  cities  on  the  dividing  lines  of  Standard  Time 
Divisions? 

6.  If  El  Paso  should  make  use  of  Mountain  Time  it  would 
have  the  time  of  what  meridian?  Would  this  be  near  the  local 
time  of  the  place? 


The  Intemational  Date  Line 

When  Magellan's  men  returned  to  Spain  from  their  voyage 
around  the  world,  they  found  that 
they  were  a  day  behind  in  their  time. 
There  must  be  some  place,  then,  where 
people  travelling  west  or  east  can  change 
a  day  in  time.  It  would  be  very  incon- 
venient for  this  change  to  be  made  in 
any  thickly  populated  area  of  the  world. 
The  nations  of  the  world  have  agreed 
upon  such  a  line  passing  along  the  180th 
meridian  with  a  few  variations  as  shown 
in  the  map.  A  person  travelling  west 
adds  a  day  to  his  calendar  when  he  crosses 
the  international  date  line.  If  he  travels 
east,  he  goes  back  a  day  on  his  calendar 
when  he  crosses  this  line. 


Exercise  10 

1.  If  a  ship  crosses  the  international  date  line  going  west 
at  11:50  p.  m.  Saturday,  how  long  will  it  be  Sunday  on  board 
the  ship? 

2.  If  a  ship  crosses  the  international  date  line  going  east  at 
midnight  Sunday,  how  long  will  it  be  Sunday  on  the  ship? 


312  EIGHTH  YEAR 

Exercise  11.    Review 

1.  The  maximum  temperature  of  a  city  during  the  summer 
of  1919  was  94°  F.  The  minimum  temperature  for  this  city  in 
the  following  winter  was  20°  F.  What  was  the  range  in  tem- 
perature in  the  city  during  that  year? 

2.  An  electric  light  company  has  the  following  system  of 
rates:  12.8  cents  per  kilowatt  for  the  first  18§  kilowatts, 
5.8  cents  per  kilowatt  for  the  next  18^  kilowatts,  and  2.8  cents 
per  kilowatt  for  all  beyond  the  first  37  kilowatts.  Find  the  hght 
bill  of  a  customer  who  used  53  kilowatts. 

3.  In  a  certain  city  gas  is  selUng  at  $1.05  per  1000  cubic 
feet.  What  is  a  customer's  gas  bill  who  uses  2800  cubic  feet 
during  one  month? 

4.  Show  how  to  read  a  gas  or  electric  meter.  Make  a  draw- 
ing of  the  dial  of  your  meter  at  home  and  use  it  to  illustrate 
how  a  meter  is  read. 

5.  The  reading  of  an  electric  meter  was '346  on  February  26 
and  370  on  March  26.  How  many  kilowatts  were  used  during 
that  month?  How  much  would  the  net  bill  for  this  month  be  if 
the  electric  ompany  charged  12§  cents  a  kilowatt  and  allowed 
a  discount  of  10%  for  prompt  payment. 

6.  The  reading  on  a  gas  meter  was  74,400  on  March  1  and 
76,800  on  April  1.  Find  the  gas  bill  for  this  month  at  $1.05 
per  1000  cubic  feet. 

7.  Washington,  D.  C,  is  approximately  75°  of  longitude  west 
of  London.  When  it  is  12  o'clock  in  London,  what  time  is  it 
in  Washington,  D.  C? 

8.  If  you  set  your  watch  at  New  York  City  and  carry  it  to 
San  Francisco  without  resetting  it,  will  it  be  too  fast  or  too 
slow?     How  much?     Why? 

9.  If  you  set  your  watch  at  Denver  and  carry  it  to  Indian- 
apolis without  resetting  it,  which  way  will  you  reset  it  and  how 
much? 


Courto'^v  Office  of  Experiment  St-itio 
U.  S.  Department  of  Agriculture 


CHAPTER  VII 
GRAPHS 

Graphs  are  used  so  extensively  to  illustrate  statistics  that  a 
knowledge  of  how  to  make  them  and  how  to  read  and  interpret 
them  should  be  obtained  by  every  one. 

The  Pictorial  Graph 

The  pictorial  graph  uses 
pictures  of  the  things  to 
be  compared,  showing  dif- 
ferences in  the  numbers 
of  the  things  by  the  relative 
sizes  of  the  pictures.  In 
the  pictorial  graph  in  the 
illustration  a  comparison  is 
made  of  the  eggs  laid  by  a  hen  the  first  year  (Fig.  1),  the  sec- 
ond year  (Fig.  2)  and  the  third  year  (Fig.  3).  Which  year  was 
the  most  productive?     How  many  eggs  did  the  hen  lay  each 

year?  The  exact  number 
of  eggs  can  not  be  told  by 
such  a  graph.  Such  a  graph 
merely  enables  us  to  get  a 
general,  impression  of  the 
numbers  compared. 

Pictorial  graphs  are  much 
improved  when  the  num- 
bers represented  by  the  pic- 
tures are  also  shown  in  the 
graph.  The  graph  at  the 
left  shows  an  improved 
type  of  pictorial  graph. 


ALFALFA  BALANCES 

THE  CORN   RATION 

HANS.  EXP.- 14  PIGS-  rao  o*ys 


CORN  «  WATER 

IN  DRV  LOT 

180  D*YS 


KANS.  BUL.  192 


Courtosy  Tntprnational  Harvester  Co. 


313 


314 


EIGHTH  YEAR 


The  Line  Graph 

A  line  graph  is  a  much  more  accurate  way  of  representing 
certain  kinds  of  statistics.  Line  graphs  are  also  much  more 
easily  made  than  pictorial  graphs. 

Suppose  that  the  wholesale  prices  of  eggs  for  a  certain  year 
are  to  be  represented  by  a  line  graph.  The  prices  averaged 
as  follows  for  the  different  months:  Jan.  30^;  Feb.  29^;  Mar. 
24^;  Apr.  18j^;  May  17^;  June  17f^;  July  17^;  Aug.  Hi)  Sept. 
19^;  Oct.  22i;  Nov.  25^;  and  Dec.  29^5. 

On  the  cross  section  paper  let  the  vertical  lines  represent  the 
different  months  and  the  horizontal  lines  represent  the  prices 
from  0  to  36,  increasing  4  cents  from  one  horizontal  line  to 
another. 

On  the  January  vertical  line  a 
dot  is  placed  half-way  between  the 
28^  line  and  the  32^  Une,  thus 
representing  30^  for  January.  On 
the  February  line  a  dot  is  placed 
one-fourth  of  the  distance  from  the 
28^  line  to  the  32^  line,  representing 
29  i  for  February.  After  the  dots 
for  all  the  months  have  been  located 
in  this  manner,  a  broken  Une  is 
drawn  to  connect  them.  This  graph  represents  very  clearly 
the  fall  and  rise  in  the  prices  of  eggs  during  that  year. 


•1     £     ; 

1- 

<      Ul     O      2     O 

'• 

> 

\ 

/ 

\ 

y 

/ 

\ 

^ 

^ 

t 

Exercise  1 

1.  From  this  graph  give  the  wholesale  prices  of  eggs  for  the 
following  months:  March,  April,  July,  September,  October, 
November  and  December. 

2.  During  what  four  months  did  the  average  price  of  eggs 
remain  the  same? 


GRAPHS 


315 


3.  How  did  the  decline  in  price  from  February  to  April 
compare  with  the  rise  in  price  from  August  to  December? 

4.  The  production  of  coal  in  long  tons  for  the  United  States 
for  the  years  1905  to  1914  was  as  follows: 


Year 

Anthracite 

Bituminous 

1905 

69,405,958 

281,239,252 

1906 

63,698,803 

306,084,481 

1907 

76,487,860 

352,408,054 

1908 

74,384,297 

296,903,826 

1909 

72,443,624 

338,987,997 

1910 

75,514,296 

372,339,703 

1911 

80,859,489 

362,195,125 

1912 

75,398,369 

401,803,934 

1913 

81,780,067 

427,190,573 

1914 

81,090,631 

377,414,259 

1905  1906  1907  1908  1909  1910  1911    1912  1913  19K» 


\ 

/ 
* 

\ 

»^ 

'' 

/ 
/ 

/ 

/ 

' 

\ 

/ 

/' 

ZW.OOO^OOO 

160,000,000 

(00.000,000 
8^000,000 

•-^ 

y 

^ 

60,OOC!,000 

Suppose  that  we  represent  the 
years  on  the  vertical  lines.  The  next 
step  is  to  determine  how  many  tons 
are  to  be  represented  by  the  distance 
from  one  horizontal  line  to  another. 
Suppose  that  we  decide  on  a  graph 
1 9  squares  high .  The  smallest  num- 
ber of  tons  is  63,698,803  and  the  largest  number  is  427,190,573, 
the  difference  between  these  numbers  being  363,491,770. 
Dividing  the  difference  by  19,  we  find  that  the  most  convenient 
number  to  represent  the  distance  from  one  horizontal  line  to 
another  is  20,000,000.  The  numbers  in  the  table  can  be  plotted 
only  approximately.  69,405,958,  the  first  number  of  tons  of 
anthracite  coal,  may  be  represented  by  a  dot  slightly  less  than 
half-way  from  the  60,000,000  Hne  to  the  80,000,000  line. 

Draw  the  graphs  for  both  anthracite  and  bituminous,  repre- 
senting the  anthracite  by  a  solid  line  and  the  bituminous  by 
a  dotted  line.  Compare  your  graph  with  the  one  in  the  book. 
In  which  one  of  these  kinds  of  coal  did  the  production  increase 
more  rapidly  during  this  period? 


S16  EIGHTH  YEAR 

6.  A  pupil  made  the  following  grades  on  his  practice  exer- 
cises for  two  weeks:  Feb.  1,  80;  Feb.  2,  87;  Feb.  5,  100;  Feb.  6, 
83;  Feb.  7,  78;  Feb.  8,  93;  Feb.  9, 100;  Feb.  12,  93;  Feb.  13,  97; 
Feb.  14,  100.    Draw  a  line  graph  to  show  his  record. 

6.  The  immigration  into  the  United  States  each  year  since 

1907  is  shown  in  the  table  at  the 

JgQg %82'870     ^^^**      -^^^^   ^   ^^^^   graph   to   show 

1909!!!     rr!    75l'786     *^^  increases  and  decreases  for  the 

1910 1,041,570     various  years.     In  what  year  during 

1911 878,587     this  period  was  immigration  largest? 

^^^2 838,172     What  year  shows  the  least  number 

1913 1,197,892        f  •        •         +  o     tt        j  4. 

.„. .  1 218  480  immigrants.^    How  do  you  account 

1915 '.'..'.......   326  700     ^^^    *^^    rapid    drop    for    the    years 

1916 298,826      1915  and  1916? 

7.  The  cost  per  pupil  for  education  in  the  United  States 

for  the  years  1901  to  1914  is 
shown  in  the  table.     Make 

1903!!!!!  22.75  1910!!!!!  33.33  »    ^^^    S^aph    to    show    the 

1904 24.14  1911 34.71  costs  for  the  various  years. 

1905 25.40  1912 36.30  What  does  the  graph  show 

1906 26.27  1913 38.31  ^bout  the  cost  per  pupil  for 

1^7 28.25  1914 39.04  ^his  period? 

8.  Keep  a  record  of  the  tt^mperature  at  9:00  o'clock  at  the 
school  house  for  a  month  and  plot  the  graph  for  the  temperature 
record  for  that  month. 

The  Bar  Graph 

The  bar  graph  is  one  of  the  easiest  to  construct  and  interpret. 
For  comparative  purposes  it  is  superior  to  other  forms  of 
graphs  because  the  size  of  a  number  is  shown  by  the  length 
of  the  bar.  Thus  only  one  dimension  has  to  be  considered, 
while  in  pictorial  graphs  two  or  three  dimensions  must  be 
considered. 


1901 $21.23      1908 $30.55 

1902 21.53      1909 31.65 


GRAPHS 


317 


ALF-AIJ-A   01T-\1H[<DS 

omm  HA\  CROPS 


The  illustration  at  the 
right  shows  a  typical  bar 
graph.  The  lengths  of  the 
bars  are  drawn  to  represent 
the  numbers  written  at  the 
right  of  each.  In  this  graph 
the  longest  bar  is  one  inch 
and  represents  5.4  tons. 
The  bar  representing  brome 
grass  (1.3  tons)  must  then 
be  drawn  approximately 
J  inch  long,  and  the  bars 

representing    the    yields     of  Courtesy  international  Harvester  Co. 

clover  and  timothy  must  be  drawn  to  the  same  scale. 


Exercise  2 

1.  Draw  a  bar  graph  showing  the  comparative  values  of 
the  products  of  the  leading  industries  in  the  United  States  for 
a  recent  year  as  shown  in  the  following  table: 

Industry  Value  of  Product 

1.  Slaughtering  and  packing $1,370,568,000 

2.  Foundries  and  machine  shops 1,228,475,000 

3.  Lumber  and  timber 1,156,129,000 

4.  Iron  and  steel 985,723,000 

6.  Flour  and  grist  mills 883,584,000 

6.  Printing  and  pubUshing. 737,876,000 

7.  Cotton  goods 628,392,000 

8.  Men's  clothing 568,077,000 

Suggestion:    A  suitable  scale  for  determining  the  length  of  the  bars 

m  the  above  problem  is  1  inch =$300,000,000. 

2.  In  1900,  40.5%  of  the  inhabitants  of  the  United  States 
were  living  in  cities  of  2500  or  more  inhabitants.  In  1910, 
46.3%  of  the  people  were  living  in  cities  of  this  size.  Show  the 
comparison  between  these  two  years  by  a  bar  graph. 


318 


EIGHTH  YEAR 


3.  Draw   a   bar   graph   representing   the   production   for 
crude  petroleum  in  the  United  States  as  shown  in  the  table: 


1904 4,916,663,682 

1905 5,658,138,360 

1906 5,312,745,312 

1907 6,976,004,070 

1908 7,498,148,910 

1909 7,649,639,508 


1910 8  801,354,016 

1911 9,258,874,422 

1912 9,328,755,156 

1913 10,434,740,660 

1914 11,162,026,470 

1915 16,806,372,368 


The  Distribution  Graph 

Another  form  of  graph  used  extensively  by  the  United  States 

government  in  its  reports 
is  the  distribution  graph. 
The  distribution  graph  in 
the  illustration  shows  the 
distribution  of  poultry  in 
the  United  States.  Each 
dot  in  this  graph  repre- 
sents 1,000,000  fowls. 
The  first  step  in  the  con- 
u.  s.  Census  Report  1910  structlou  of  such  a  graph  is 

to  determine  the  number  for  each  dot.  Then  determine  the 
number  of  dots  for  each  state  and  arrange  them  in  some  syste- 
matic order.  From  the  distribution  graph  for  poultry,  name  the 
chief  poultry-producing  states  in  our  country. 


Exercise  3 

1.  Find  the  population  for  each  county  in  your  state  and 
make  a  distribution  graph  showing  the  distribution  of  popula- 
tion in  your  state. 

2.  On  a  map  of  the  United  States  draw  a  distribution  graph 
showing  the  distribution  of  horses  in  the  United  States  according 
to  the  census  of  1910,  which  was  as  follows: 


GRAPHS 


319 


Iowa 

.1,449,652 

Illinois 

.1,402,649 

Texas 

.1,125,834 

Kansas 

.1,099,738 

Missouri .  . . 

.  1,035,884 

Nebraska.  . 

.    971,279 

Ohio 

.    888,027 

Indiana. . . . 

.    785,954 

Minnesota. . 

.    738,578 

Oklahoma. . 

.    708,848 

S.  Dakota. . 

.    645,639 

N.  Dakota . 

.    625,984 

Wisconsin . . 

.    608,657 

Michigan.  . 

.    602,410 

New  York . 

.    587,393 

Pennsylvania   542,793 


California 445,849 

Kentucky 425,884 

Tennessee 333,025 

Virginia 318,831 

Montana 304,239 

Colorado 284,647 

Washington...  269,501 

Oregon 261,627 

Arkansas 245,861 

Mississippi....  210,937 

Idaho 189,322 

West  Virginia.  176,530 

Louisiana 175,814 

New  Mexico .  .  175,057 
N.Carolina...  162,783 
Wyoming 150,984 


Maryland 150,159 

Alabama 132,611 

Georgia 118,583 

Utah 111,135 

Maine 107,210 

Arizona 93,803 

New  Jersey . . .  88,239 

Vermont 80,556 

South  Carolina  79,105 

Nevada 65,717 

Massachusetts.  64,109 
Connecticut...  46,248 

N.  H 46,154 

Florida 45,029 

Delaware 31,943 

Rhode  Island.     9,527 


Plan  your  numbers  so  that  you  will  get  at  least  one  dot  for  Rhode 
Island.  Make  your  number  per  dot  as  large  as  possible,  however,  so  that 
there  will  not  be  so  many  dots  for  the  states  containing  large  numbers. 


The  Circle  Graph 

The  circle  graph  at  the  right  rep- 
resents the  approximate  per  cents 
of  the  different  food  substances  in 
peanuts. 

The  circumference  of  a  circle  is 
divided  into  360  equal  parts  called 
degrees.  The  angle  showing  the  pro- 
portion of  fat  cuts  off  29.1%  of  360  degrees  (360°)  or  104.76°. 

1.  Find  the  number  of  degrees  in  the  angles  for  each  of 
the  other  food  substances  in  the  peanut. 

2.  In  alfalfa  65%  of  the  food  value  is  in  the  leaves  and 

35%  in  the  stem.    Draw  a  circle  graph  to  show  the  relative 

proportions  of  each.      Use  a  protractor  to  lay  out  the  angles. 

A  large  amount  of  graphing  can  be  done  to  advantage  in  connection 
with  geography  and  thus  broaden  the  practice  work  in  arithmetic. 


CHAPTER  Vni 

THE  METRIC  SYSTEM 

Weights  and  Measures 

Over  a  century  ago,  in  the  time  of  the  French  Revolution, 
a  commission  of  able  men  was  formed  to  devise  a  convenient 
system  of  weights  and  measures  to  replace  the  clumsy  systems 
then  in  use  in  the  countries  of  Europe.  They  proposed  the 
metric  system,  a  scheme  so  scientific  in  plan  and  so  convenient 
in  its  use  that  it  has  grown  in  favor  over  the  world,  until  now 
it  is  used  around  the  globe,  except  among  the  English-speaking 
peoples.  Even  in  the  United  States  and  in  the  British  Empire 
it  is  in  use  in  a  limited  way,  being  employed  very  generally 
in  scientific  laboratories  and  is  recognized  by  law. 

The  need  for  a  more  general  knowledge  of  this  system  in 
this  country  is  growing  from  day  to  day,  in  view  of  our  increas- 
ing trade  with  the  nations  which  use  it  exclusively.  Without 
mastering  it  we  cannot  readily  understand  the  trade  catalogues 
of  their  business  houses  or  the  bills  sent  us  for  articles  purchased ; 
nor  can  we  make  them  readily  understand  our  own  price  lists 
and  bills  of  goods  sold  to  them  without  writing  these  in  terms 
of  the  metric  system.  No  ambitious  pupil  of  the  present  day 
can  afford  to  slight  the  metric  system  in  his  study  of  arithmetic. 

This  commission  measured  very  carefully  a  portion  of  the 
meridian  running  through  Paris  and  estimated,  from  this 
measurement,  the  distance  from  the  North  Pole  to  the  Equator. 
They  then  took  one  ten-millionth  of  this  distance  as  the  stand- 
ard measure  for  length  and  named  it  the  meter. 

Since  they  wished  to  base  their  scheme  upon  a  decimal  ratio, 
they  selected  the  Greek  prefixes  deka,  meaning  ten;  hekto, 

320 


THE  METRIC  SYSTEM 


321 


meaning  hundred;  kilo,  meaning  thousand,  and  myria,  meaning 
ten  thousand,  for  the  multiples  of  any  unit  of  measure,  and  the 
Latin  prefixes  deci,  meaning  j^;  centi,  meaning  ^^  5  and  milli, 
meaning  y^oo"'  ^^r  the  fractions  of  any  unit  of  measure. 

Instead  of  learning  an  entirely  new  set  of  names  for  each  table 
as  we  have  to  do  in  our  clumsy  English  system  of  weights  and 
measures,  all  we  have  to  do  in  the  metric  system  is  to  learn  one 
new  unit  for  each  table,  and,  by  prefixing  the  roots,  the  new 
tables  can  be  formed. 

Metric  Table  of  Length 

=  1  centimeter (cm.) 

=  1  decimeter (dm.) 

=  1  meter (m.) 

=  1  dekameter (Dm.) 

=  1  hektometer (Hm.) 

=  1  kilometer (Km.) 

10  kilometers =1  myriameter (Mm.) 

The  following  is  an  illustration  of  a  decimeter  divided  into 
10  equal  parts  called  centimeters  (cm.).  Each  of  these  centi- 
meters is  also  divided  into  10  equal  parts  called  millim£ters 
(mm.).  Along  the  base  of  the  ruler  is  shown  a  scale  in  inches. 
This  shows  that  a  decimeter  is  slightly  less  than  4  inches. 
A  meter  =  39.37  inches.  \ 


10  millimeters  (mm) . 

10  centimeters 

10  decimeters 

10  meters 

10  dekameters 

10  hektometers 


Exercise  1 

1.  A  meter  stick  is  how  many  times  as  long  as  the  decimeter 
shown  above? 

2.  If  you  have  access  to  a  work  shop,  construct  a  meter 
stick  from  another  as  a  model  or  use  the  scale  in  your  book. 


322  EIGHTH  YEAR 

3.  A  meter  equals  how  many  centimeters? 

4.  A  dekameter  is  equal  to  how  many  meters? 
6.  A  kilometer  is  equal  to  how  many  meters? 
6.  Change  355  millimeters  to  centimeters. 

Since  10  millimeters  =  1  cm.,  355  mm.  =355  mm. -J- 10  mm.  =35.5,  the 
number  of  cm.  This  shows  the  convenience  of  the  metric  system  in  chang- 
ing from  one  unit  to  another — we  merely  move  the  decimal  point  to  the 
right  or  left  the  required  number  of  places. 

7   Change  8750  mm.  to  meters. 

8.  Change  .5  km.  to  Dm. 

9.  Change  345  meters  to  km. 

10.  A  rod  in  our  English  system  is  equal  to  how  many  meters? 

11.  Find  the  length  and  width  of  your  school  room  in  meters. 

12.  Measure  the  length  and  width  of  your  desk  in  centimeters. 

13.  Draw  a  line  on  the  blackboard  a  meter  in  length  without 
looking  at  a  meter  stick.  Now  measure  it  and  see  how  many 
centimeters  you  have  missed  it. 

14.  Measure  the  lengths  of  objects  in  your  school  room  after 
you  have  first  estimated  their  length,  using  the  different  units 
meter,  decimeter  and  centimeter  in  your  estimates. 

16.  A  kilometer  is  equal  to  what  decimal  fraction  of  a  mile? 

In  France  they  estimate  the  distance  between  two  cities  in  kilometers 
instead  of  miles  as  we  do  here. 

Metric  Table  of  Square  Measure 

The  square  centimeter  is  one  of  the  most  common  of 
the  units  of  square  measure  in  scientific  work.     As 
shown  in  the  exact  reproduction  at  the  left,  it  is  a 
square  1  cm.  on  each  side. 

Find  the  number  of  square  centimeters  in  a  square  inch. 


laOUARE 

ComntTER 


■/ 


THE  METRIC  SYSTEM     /  323 

100  sq.  millimeters  (sq.  mm.)  =1  sq.  centimeter. 
100  sq.  centimeters  (sq.    cm.)  =  l  sq.  decimeter. 
100  sq.  decimeters    (sq.  dm.)  =  l  sq.  meter  (sq.  m.). 

For  measuring  land  the  following  units  are  used: 

1  sq.  meter  =  1  centare  (ca.). 
100  centares  =1  are  (a.). 
100  ares  =1  hectare  (Ha.). 

A  hectare  is  equal  to  about  2.471  acres. 

Exercise  2 

1.  What  is  the  area  of  the  top  of  your  desk  in  square 
centimeters? 

2.  Draw  a  square  meter  on  the  floor  without  using  a  meter 
stick.  Use  the  meter  stick  to  check  your  estimated  square 
meter. 

3.  A  friend  of  mine  in  Argentina  writes  that  he  has  planted 
20  hectares  of  wheat.   How  many  acres  of  wheat  has  he  planted? 

4.  What  part  of  an  acre  is  an  are? 

5.  Reduce  45675  sq.  mm.  to  square  meters.  (Remember 
that  the  multiplier  is  100  in  square  measure  instead  of  10.) 

6.  Make  5  problems  that  involve  square  measure. 

Metric  Table  of  Volume 


1 

cu.  cm. 


1000  cu.  millimeters  (cu.  mm.)  =  1  cu.  centimeter. 
1000  cu.  centimeters  (cu.   cm.)  =  1  cu.  decimeter. 
1000  cu.  decimeters  (cu.  dm.)  =  1  cu.  meter. 
In  measuring  wood  a  cubic  meter  is  called  a  stere. 

A  cubic  centimeter  is  a  cube  1  cm.  long,  1  cm.  wide  and  1  cm. 
high.  The  exact  size  of  a  cubic  cm.  is  shown  in  the  illustration 
at  the  right. 

Find  the  number  of  cubic  centimeters  in  a  cubic  inch.  1  cu. 
cm.  is  what  part  of  1  cu.  in.? 


T 


324  EIGHTH  YEAR 

Exercise  3 

1.  Make  a  cube  1  decimeter  long,  1 
decimeter'  wide  and  1  decimeter  high.  An 
open  cubical  box  may  be  made  by  making 
each  line  in  the  pattern  shown  at  the  left 
I  decimeter  long.  The  four  sides  may  be 
turned  up  at  the  dotted  lines  and  the  corners 
Hdm-H  sewed  or  pasted  together  with  some  kind  of 

gummed  paper. 

2.  In  a  stere  are  how  many  cubic  centimeters  of  wood? 

8.  A  shipment  of  guanacaste  wood  from  Central  America 
forms  a  pile  two  meters  high,  1  meter  broad  and  30  meters 
long.     How  many  dekasteres  does  it  contain? 

4.  How  many  cubic  meters  of  earth  are  removed  to  make  an 
excavation  12  meters  long,  8  meters  wide  and  1.5  meters  deep? 

5.  What  will  be  the  cost  of  teaming  in  the  removal  of  2500 
cubic  decimeters  of  gravel  at  $1  per  cubic  meter? 

6.  A  cubic  meter  is  equal  to  about  1.3  cubic  yards.  How- 
many  cubic  yards  would  there  be  in  the  excavation  described 
in  Problem  4? 

Metric  Table  of  Capacity 

The  cubical  box  described  in  Problem  1  of  the  preceding 
exercise  if  made  correctly  will  hold  exactly  1  cubic  decimeter. 
This  is  taken  as  the  unit  of  capacity  and  called  the  liter  (lee-ter). 
A  liter  is  equal  to  about  1.057  quarts. 

10 milliliters  (ml.) =1  centiliter (cl.) 

lOcentUiters =1  deciliter (dl.) 

lOdeciliters =1  liter (1.) 

10  liters =1  dekaliter (DL) 

lOdekaliters =1  hektoliter (HI.) 

lOhektoliters =1  kiloliter (Kl.) 


THE  METRIC  SYSTEM  325 

Exercise  4 

1.  How  many  cubic  centimeters  are  there  in  a  liter? 

2.  If  milk  costs  8  cents  per  liter,  what  is  the  cost  of  a  deka- 
liter of  milk? 

3.  Reduce  8  dekaliters  to  deciliters. 

4.  An  aquarium  2  meters  long,  1^  meters  broad  and  1 
meter  deep  contains  how  many  liters? 

5.  A  bin  in  a  certain  granary  is  4  meters  long,  3  meters 
broad  and  175  centimeters  deep.  How  many  hektoliters  does 
it  contain? 

6.  A  hektoliter  is  equal  to  about  2.837  bushels.  How  many 
bushels  of  wheat  will  the  bin  described  in  Problem  5  hold? 

7.  Change  245  liters  to  hektoliters. 

8.  Make  4  problems  involving  the  metric  table  of  capacity. 

Metric  Table  of  Weight  ^,B=^5?^-^a»^ 

If  a  cubic  centimeter  of  distilled  water  be  HnTlj  j, 

weighed  at  a  temperature  of  39°  F.  it  will  I  n  '^"-^ 

weigh    exactly    a    gram.      1000    of    these  I 

grams  make  a  kilogram  (or  kilo  for  short).  I 

A  kilogram,  then,  is  the  weight  of  a  cubic  I  II  JOOC 

decimeter   or   liter   of   distilled   water   at  IHGRAr' 

the  temperature  of  39°  Fahrenheit.     \ 

10  milligrams  (mg.) =1  centigram (eg.) 

10  centigrams =1  decigram (dg.) 

10  decigrams =1  gram (g.) 

10  grams =1  dekagram (Dg-) 

10  dekagrams =1  hektogram (Hg.) 

10  hektograms =1  kilogram (Kg.) 

10  kilograms =1  mjTiagram (Mg.) 

10  myriagrams =1  quintal (Q.) 

10  quintals =1  Metric  Ton (MT.) 


326  EIGHTH  YEAR 

Exercise  6 
A  kilogram  is  equal  to  about  2.204  pounds. 

1.  A  gram  is  equal  to  how  many  centigrams? 

2.  A  kilogram  is  equal  to  how  many  grams? 

3.  How  many  grams  are  there  in  a  metric  ton? 

4.  How  many  pounds  are  equal  to  a  metric  ton? 

5.  Linseed  oil  is  only  .935  as  heavy  as  distilled  water. 
How  many  grams  will  a  liter  of  linseed  oil  weigh? 

6.  Gasoline  is  only  .7  as  heavy  as  distilled  water.  How 
much  will  a  liter  of  gasoline  weigh? 

7.  I  weighed  myself  on  a  standard  metric  scale  in  a  phy- 
sician's office  and  found  my  weight  74  kilograms.  Find  my 
weight  in  pounds. 

8.  The  average  weight^  of  boys  13 1-  years  old  is  38.48 
kilograms.    Find  their  average  weight  in  pounds. 

9.  The  average  weight  of  girls  13^  years  old  is  40.24 
kilograms.     Find  their  average  weight  in  pounds. 

10.  How  many  pounds  do  you  weigh?  Express  this  weight  in 
kilograms. 

11.  A  farmer  in  Argentina  measures  his  wheat  by  the  hekto- 
liter.  A  hektoliter  =  2.837  bushels.  A  bushel  of  wheat  weighs 
60  pounds.  From  these  facts  find  the  weight  of  a  hektoliter 
of  wheat  in  kilograms. 

12.  A  cubic  decimeter  of  gold  weighs  19.3  kilograms.  How 
many  pounds  avoirdupois  weight  does  a  cubic  decimeter  of 
gold  weigh? 

13.  A  cubic  foot  of  water  weighs  62.5  pounds.  How  many 
kilograms  are  there  in  the  weight  of  a  cubic  foot  of  water? 

14.  Make  three  problems  which  involve  the  metric  table 
of  weights. 

»From  Table  B,  Rowe's  "Physical  Nature  of  the  Child." 


THE  METRIC  SYSTEM  327 

Exercise  6 

From  the  information  already  given  in  connection  with  the 
metric  system  find  the  following  equivalents : 

1.  A  meter  =  ?  feet?  6.  A  quart  =  ?  cu.  in.? 

2.  An  inch  =  ?  cm.?  7.  A  cu.  meter  =  ?  cu.  ft.? 

3.  A  mile  =  ?  km.?  8.  A  pound  =  ?  grams? 

4.  An  acre  =  ?  sq.  yd.?  9.  A  cu.  in.  =  ?  cu.  cm.? 

5.  A  gallon  =  ?  liters?  10.  A  rod  =  ?  meters? 

Exercise  7 

1.  A  book  is  4  centimeters  thick  between  the  covers.  It 
contains  400  pages.  How  many  leaves  are  there  in  1  millimeter 
of  thickness? 

2.  Sound  travels  in  the  air  at  the  rate  of  1087  feet  per  sec- 
ond.    Find  the  speed  of  sound  in  meters  per  second. 

3.  How  many  seconds  would  elapse  between  the  flash  and 
the.  report  of  a  gun,  if  I  were  a  kilometer  away? 

4.  An  American  soldier  bought  3  liters  of  milk  of  a  French 
farmer.     How  many  quarts  of  milk  did  he  buy? 

6.  The  German  army  advanced  on  one  march  until  they 
were  5  kilometers  from  Amiens.  How  many  miles  were  they 
from  that  city? 

6.  The  French  have  a  cannon  called  the  "75."  This  means 
that  the  diameter  of  the  bore  is  75  mm.  Express  this  diameter 
in  inches. 

7.  Measure  your  height  in  inches.  Find  your  height  in  cen- 
timeters.    Express  your  height  in  meters. 

8.  The  distance  between  two  Belgian  cities  is  32  kilometers. 
What  is  the  distance  in  miles  between  these  cities. 


328 


EIGHTH  YEAR 


Foreign  Money 

The  participation  of 
our  soldiers  in  the 
World  War  has  made 
the  subject  of  foreign 
money  of  a  great 
deal  of  interest.  Many 
of  these  soldiers  have 
brought  back  foreign 
coins  as  souvenirs  of 
the  war.  If  you  can 
get  any  foreign  coins 
or  bills,  bring  them  to 
school  and  place  them 
on  exhibit  for  the 
class. 

During  the  war  the 
value  of  many  of  these 
coins  and  bills  became 

much  lower  in  terms  of  U.  S.  money  than  their  regular  value. 

Find  the  present  values  of  as  many  as  possible. 


Coimtry 

Money 
Unit 

Regular  Value 
in  U.  S.  Money 

Present  Value 
in  U.  S.  Money 

Equiv.  in 
Lower  Coins 

Great  Britian 
Germany .... 

France 

Austria 

Italy 

Spain 

Holland 

Russia 

Japan 

Portugal .... 

Brazil 

Greece 

Norway 

pound  (£) 

mark 

franc 

krone 

lira 

peseta 

guilder 

ruble 

yen 

milreis 

milreis 

drachma 

krone 

$4.8665 
.238 
.193 
.203 
.193 
.193 
.402 
.515 
.498 
1.08 
.546 
.193 
.268 

? 
? 

? 
? 
? 
? 
? 

? 
? 

? 
? 
? 
? 

20  shillings 
100  pfennigs 
100  centimes 
100  heller 
100  centisimi 
100  centimos 
100  gulden 
100  kopeks 
100  sen 
1000  reis 
1000  reis 
100  leptas 
100  ore 

FOREIGN  MONEY  329 

Exercise  1 

1.  How  many  shillings  are  there  in  3  pounds  4  shillings? 

2.  What  is  the  value  in  U.  S.  money  of  £20? 

3.  What  is  the  value  in  English  money  of  $486.65? 

4.  What  is  the  value  in  U.  S.  money  of  a  shilling? 

5.  12  pence  =  1  shiUing.  What  is  the  value  in  U.  S.  money 
of  an  EngUsh  penny? 

6.  Reduce  to  U.  S.  money  2  francs  45  centimes. 
Solution:     1  franc  =  $.193.      2  francs  45  centimes  =  2.45  X 

$.193  =  $.47285  or  47  cents  in  U.  S.  money.     • 

7.  What  is  the  sum  of  4  francs  5  centimes;  6  francs  15 
centimes;  25  francs  10  centimes;  and  15  francs  75  centimes? 
What  is  the  value  of  this  sum  in  U.  S.  money? 

8.  What  is  the  sum  of  20  marks  15  pfennig;  42  marks 
25  pfennig;  68  marks  40  pfennig;  and  12  marks  20  pfennig? 
Express  the  value  of  this  sum  in  U.  S.  money. 

9.  Add  14  pesetas  10  centimos;  16  pesetas  18  centimos; 
25  pesetas  14  centimos;  and  25  pesetas  58  centimos.  Find  the 
value  of  this  sum  in  our  money. 

10.  Add  60  yen  30  sen;  45  yen  15  sen;  26  yen  45  sen; 
and  14  yen  20  sen.  What  is  their  exact  equivalent  in  our 
money? 

11.  If  a  friend  in  Rio  de  Janiero  writes  that  he  has  invested 
5000  milreis  in  a  coffee  plantation,  how  much  do  I  know  that  he 
has  invested  in  U.  S.  money? 

.12.  If  a  "Jackie"  bought  a  souvenir  in  Paris  for  2  francs  50 
centimes,  another  at  Rome  for  4  lira  10  centisimi,  and  one  at 
Barcelona  for  3  pesetas  50  centimos,  what  was  the  amount  in 
U.  S.  money  which  he  paid  for  the  three  souvenirs?  (Use 
regular  values.) 

13.  A  traveler  bought  a  set  of  Japanese  dishes  in  Tokio  for 
96  yen.    Find  the  cost  of  the  dishes  in  U.  S.  money. 


330  EIGHTH  YEAR 

General  Review  Problems 

1.  A  boy  in  a  shop  wishes  to  find  the  center  of  a  board  16f 
inches  long.     How  far  from  each  end  is  the  center? 

2.  How  many  pieces  of  ribbon  1^  feet  long  can  be  cut  from 
a  10-yard  bolt  of  ribbon? 

3.  Find  the  cost  of  5§  yards  of  dress  goods  at  $1.37^  a  yard. 

4.  Mr.  Johnson  bought  a  house  for  $3200  and  sold  it  for 
$3800.      Find  his  per  cent  of  gain. 

5.  What  is  the  interest  on  $75  for  90  days  at  6%? 

6.  A  suit  marked  $56.50  is  placed  on  sale  at  a  reduction  of 
20%.     What  is  the  sale  price  on  this  suit? 

7.  A  grocer  bought  eggs  for  36  cents  a  dozen  and  retailed 
them  at  39  cents  a  dozen.     What  was  his  per  cent  of  profif 

8.  A  four-room  flat  renting  for  $35  per  month  was  increased 
to  $45  a  month.  What  was  the  yearly  increase  in  rent?  What 
was  the  per  cent  of  increase  in  rent? 

9.  A  corporation  distributed  a  profit  of  $40,000  on  a  dividend 
of  8%.  What  was  the  value  of  the  capital  stock  of  this  cor- 
poration? 

10.  A  merchant  was  allowed  a  discount  of  3%  for  a  cash  pay- 
ment on  a  bill  of  $32.40.     Find  the  net  amount  of  the  bill. 

11.  A  broker  sold  a  carload  of  95  hogs  averaging  240  pounds 
at  $10.00  per  carload  of  19,000  lbs.  and  5  cents  per  hundred  in 
excess  of  that  weight.     What  was  his  conunission? 

12.  Mr.  Coppins  bought  a  piano  listed  at  $650  at  discounts 
of  25%  and  10%.     What  was  the  net  price  of  the  piano? 

13.  Find  the  interest  on  $180  for  1  year  5  months  and  12 
days  at  6%. 

14.  An  agent  received  a  commission  of  25%  for  introducing 
an  electric  cleaner  in  a  community.  His  sales  amounted  to  $285. 
What  was  his  commission? 


GENERAL  REVIEW  PROBLEMS  331 

15.  A  real  estate  agent  sold  a  farm  for  $28,750  on  a  commis- 
sion of  2%.     How  much  did  the  owner  receive? 

16.  Find  the  income  tax  of  a  married  man  with  an  income 
of  $3750,  allowing  additional  exemptions  for  3  children, 

17.  A  man  25  years  of  age  takes  out  a  20-year  endowment 
policy  for  $4000.     What  was  his  yearly  premium  on  this  policy? 

18.  Find  the  area  of  a  triangular  strip  of  land  with  a  base  of 
20  rods  and  an  altitude  of  16  rods. 

19.  A  boy  raised  corn  on  a  rectangular  piece  of  ground  132 
feet  long  and  99  feet  wide.  He  raised  24  bushels  of  corn  on 
this  plot.     Compute  his  yield  per  acre  at  the  same  rate. 

20.  The  area  of  the  six  New  England  States  are  as  follows: 
Maine,  33,040  square  miles;  N.  H.,  9341;  Vermont,  9504; 
Mass.,  8266;  Rhode  Island,  1248;  Conn.,  4965.  What  is  the 
total  area  of  the  New  England  States? 

21.  Find  the  cost  of  2340  board  feet  of  lumber  at  $85.00  a 
thousand. 

22.  Ellen  missed  2  problems  out  of  25  on  an  arithmetic  paper. 
Find  her  grade  on  the  scale  of  100  for  a  perfect  paper  and  count- 
ing all  of  the  problems  of  equal  difficulty. 

23.  Explain  the  difference  in  a  blank  indorsement  and  an 
"indorsement  in  full"  of  a  check. 

z^.  What  is  the  bank  discount  on  a  note  for  $350  for  a  period 
of  60  days  at  a  rate  of  6%? 

25.  What  will  20  shares  of  stock  quoted  at  83^  cost  if  the 
broker  charges  \%  commission? 

26.  What  will  be  the  per  cent  of  income  on  a  bond  bought 
at  90  (including  brokerage)  if  the  owner  receives  a  dividend  of 
$7.20? 

27.  Extract  the  square  root  of  43,296. 

28.  A  rectangular  field  containing  20  acres  is  80  rods  long. 
How  many  rods  of  fence  must  a  farmer  buy  to  enclose  it? 


SUPPLEMENT 

The  purpose  of  this  section  is  to  provide  additional  work  in 
simple  equations  to  supplement  Chapter  III  of  Part  I,  and  to 
give  material  for  additional  work  in  measurements  in  con- 
nection with  Chapter  IV  of  Part  II. 

While  this  section  is  intended  to  be  optional,  it  offers  valuable 
training  in  preparation  for  algebra  and  geometry  and  should 
be  used  when  time  permits. 

I.  SIMILAR  FIGURES 

Similar  figures  are  figures  having  the  same  shape. 

All  squares  are  similar  to  each  other  because  they  all  have 
the  same  shape.  In  the  same  way  all  circles  are  similar.  All 
rectangles  are  not  similar  to  each  other.  Rectangles  A  and  B 
are  similar  to  each  other  because  they  have  the  same  shape, 


QD 


each  being  twice  as  long  as  wide.  Rectangles  B  and  C  are 
not  similar  because  C  is  5  times  as  long  as  it  is  wide  and  B  is 
only  2  times  as  long  as  it  is  wide. 

Exercise  1.    Ratio  and  Proportion 

Ratio  and  proportion  are  very  convenient  tools  to  work  with 
in  discussing  similar  figures.  It  will  be  to  our  advantage, 
then,  to  master  the  uses  of  these  tools  before  going  further 
into  the  study  of  similar  figures. 

The  railo  of  one  number  to  another  is  the  number  of  times 
the  first  contains  the  second. 

332 


SIMILAR  FIGURES  333 

The  ratio  of  15  to  3  is  the  number  of  times  15  contains  3, 
which  equals  5.  The  ratio  of  15  to  3  may  be  expressed  as 
follows:  15  :  3  reads  "the  ratio  of  15  to  3"  or  ^.  The  fraction 
is  an  excellent  way  of  expressing  a  ratio  because  it  indicates 
the  division  idea  of  a  ratio.    ■^,  the  ratio  of  15  to  3  =  15^3  =  5. 

A  statement  that  two  ratios  are  equal  is  called  a  proportion 
as  15  :  5  =  24  :  8.  The  four  numbers  in  this  proportion  are 
called  the  terms  of  the  proportion.  The  first  and  last  terms  of 
a  proportion  are  called  the  extremes  and  the  second  and  third 
terms  are  called  the  means.  15  and  8  are  the  extremes  of  the 
above  proportion  and  5  and  24  are  the  means. 

What  is  the  product  of  the  extremes,  15  and  8? 
What  is  the  product  of  the  means,  5  and  24? 
How  does  the  product  of  the  means  compare  with  the  product 
of  the  extremes  of  the  proportion? 

See  if  the  same  relation  exists  between  the  products  of  the 
means  and  extremes  in  the  following  proportions: 


1. 

10  : 

5=  8 

4. 

5. 

18 

6  =  15  : 

5. 

2. 

60: 

15  =  12 

3. 

6. 

30 

6  =  25  : 

5. 

3. 

48: 

8  =  12 

2. 

7. 

15 

7=45: 

21. 

4. 

4  : 

2  =  36 

18. 

8. 

6 

5  =  18. 

15. 

If  we  should  try  a  very  large  number  of  these  proportions, 
we  should  find  that  the  same  relation  holds  true.  This  relation 
may  be  expressed  in  the 

PRINCIPLE:    In  any  proportion  the  product  of  the  means  is 
equal  to  the  product  of  the  extremes. 

If  one  term  of  a  proportion  is  unknown,  by  means  of  this 

principle  the  unknown  term  can  be  found.    Let  X  represent 

the  unknown  term.^ 

•By  putting  the  value  of  the  unknown  term  in  place  of  X  after  it  has 
been  found  and  then  finding  whether  the  product  of  the  means  equals 
the  product  of  the  extremes,  a  check  upon  the  correctness  of  the  work  is 
shown. 


334  EIGHTH  YEAR 

40  :  X  =  24  :  3 
24XX  or  24X  =  product  of  the  means. 
40  X  3  =  120  =  product  of  the  extremes. 
Therefore:    24X=120 


(Check:    40  :  5=  24  :  3) 
120  =  120 

Exercise  2 
Find  the  value  of  X  in  each  proportion: 

1.  27:12=  X:   8.       6.  21  :  18=  56:  X.  11.    9:   3=X:   6 

2.  14:X  =  26:13.  7.  X:  28=10:  7.  12.  X:  12  =  20:  5 
3.35:  7  =  15:  X.  8.  3.5:  2.5  =  .21:  X.  13.16:  6=X:18 
4.  X:  7  =  36:  6.  9.  9  :  5=X:10.  14.  21:X=14:  8 
6.  18:12=  X:   6.      10.    8:   X=  16:   8.  15.    f:f  =  X:f 

PRINCIPLE:    In  similar  figures  the  corresponding  dimensions 
are  proportional, 
c 


If  the  triangles  ABC  and  M  N  O  are  similar  (that  is,  the 
same  shape),  the  corresponding  dimensions  are  proportional: 

AB  :  MN  =  CD  :  OP 

Exercise  3 

1.  Suppose  A  B  =  16  inches;  N  M  =  10  inches;  C  D  =  6  inches. 
Find  O  P. 
Solution:     Put  those  values  in  the  above  proportion: 
16  :  10  =  6  :  X. 

16X  =  60  (the  product  of  the  extremes  =  product 
of  means). 
X=ff  or  3 J.    Therefore:    0  P  or  X  =  3|  in. 


SIMILAR  FIGURES  335 

2.  Two  rectangles  are  similar.  The  base  of  the  first  is 
12  inches,  the  base  of  the  second  is  8  inches  and  the  altitude 
of  the  second  is  6  inches.    What  is  the  altitude  of  the  first? 

Caution:   Be  sure  to  keep  the  right  order — base  of  1st  :  base 
of  2nd  =  alt.  of  1st  :  alt.  of  2nd. 

3.  In  the  above  triangles  A  B  =  16  inches,  MN  =  10  inches 
and  A  C  =  7  inches.    Find  the  side  M  O. 

Exercise  4.     Similar  Triangles 

1.  To  measure  the  height  of  a  tree, 
c  Method:     Measure  the  shadow 

A  B  of  the  tree.  Set  up  a  stick  F  D 
whose  length  you  have  measured, 
so  that  it  is  perpendicular  to  the 

j^ surface  of  the  ground.    Measure  the 

'  shadow  of  this  stick. 

The  triangles  ABC  and  D  E  F  are  similar. 
The  shadow  of  tree  A  B  :  shadow  of  stick  D  E  =  height  of 
tree  A  C  :  height  of  stick  F  D. 

2.  If  A  B  =  30  feet;  D  E  =  22  inches  and  D  F=36  inches, 
find  the  height  of  the  tree. 

Caution:    Both  expressions  in  the  same  ratio  must  be  ex- 
pressed in  the  same  unit  of  measure. 

3.  A  tree  casts  a  shadow  42  feet  long.  At  the  same  time 
a  stick  5  feet  high  casts  a  shadow  3  feet  long.  How  high  is 
the  tree? 

4.  Another  method  of  measuring  the  height  of  the  tree 
^  is  to  construct  a  large  right  triangle  out 

of  strips  of  lumber.  Make  it  so  that  the 
legs  of  the  right  triangle  are  3  and  4  feet 
long.  If  equal  legs  are  put  on  this  triangle 
it  is  much  easier  to  make  the  accurate 
measurements. 


336 


EIGHTH  YEAR 


Move  the  triangle  back  and  forth  until  a  person  with  his 
eye  at  B  can  just  see  the  top  of  the  tree  along  the  edge  D  B. 
Measure  the  distance  from  B  to  the  tree.  ABE  and  D  C  B 
are  similar  triangles.  The  length  of  the  legs  of  the  triangle 
measuring  instrument  must  be  added  to  A  E  to  give  the  whole 
height  A  E. 

6.  Suppose  A  B  =  50  feet,  B  C  =  3  feet  and  D  C=4  feet, 
what  is  the  height  of  the  tree?   Allow  3  feet  for  the  legs. 

6.  To  measure  the  distance  across  a  pond. 
Measure  B  C,  D  C  and  E  D. 
Triangles   ABC   and   D  C  E   are 

similar. 
ThenBC  :  DC  =  AB  :  ED. 
Suppose  BC  =  150  feet;  D  C  =  90 
feet;  and  E  D  =  50  feet.    Find  A  B. 

7.  To  measure  the  width  of  a  stream. 

Select  some  object  such 
as  a  tree  on  the  opposite 
bank  at  B.  Set  a  stake  at 
A  and  lay  off  a  line  A  D. 
Lay  off  D  C  as  nearly  par- 
allel to  A  B  as  possible. 
Set  a  stake  at  any  point  O 
in  the  Une  A  D.  Move. 
back  along  the  line  D  C  until  the  stake  at  0  is  in  line  with  the 
tree  at  B.  Set  a  stake  at  this  point  C.  Measure  A  O,  O  D 
and  D  C.    The  triangles  A  O  B  and  COD  are  similar. 

By  means  of  this  pair  of  similar  triangles  we  get  the  pro- 
portion: 

AB  :  CD  =  AO  :  O  D. 

8.  If  CD  =  100  feet,  A  0  =  50  feet    and    O  D  =  25  feet, 
find  A  B,  the  width  of  the  stream. 


SIMILAR  FIGURES 


337 


9.  A  boy  desiring  to  measure  the  width  of  an  impassable 
river  flowing  through  level  land  drew  on  the  edge  of  the  bank, 
parallel  with  the  stream,  a  base  line,  at  each  end  of  which 
he  drove  a  stake  to  which  he  attached  the  end  of  a  ball  of 
twine.  At  one  end  of  the  base  line,  with  an  instrument,  he 
sighted  a  small  spot  in  a  rock  on  the  opposite  bank,  and  noted 
the  angle  made  by  the 
line  of  sight  with  the  base 
line.  He  then  turned  his 
instrument  to  an  equal 
angle  on  the  other  side 
of  the  base  line,  and  had 
an  assistant  carry  the  twine 
a  long  way  along  the  line  f''  ""*•* 

of    sight.      At    the    other 

end  of  the  base  line  he  sighted  the  same  spot  in  the  rock, 
then  turned  his  instrument  to  an  equal  angle  on  the  other 
side  of  the  base  Une,  and  had  his  assistant  carry  the  second 
ball  of  twine  along  the  line  of  sight.  From  the  point  where 
the  strings  crossed,  he  measured  straight  to  the  base  line, 
and  announced  the  measure  as  being  that  of  the  width  of 
the  stream.    Was  this  correct?    Explain  your  answer. 

10.  By  placing  a  mirror  on  the 
ground  and  moving  up  or  back 
until  the  top  of  the  object  to  be 
measured  is  seen  in  the  mirror,  the 
height  of  any  object  can  be  found. 
ABC  and  B  D  E  are  similar  triangles  and  C  A  distance  from 
the  eye  to  the  ground;  A  B,  the  distance  from  one's  feet  to  the 
mirror  =  D  E,  the  height  of  the  object  :  B  D  the  distance  of 
the  mirror  from  the  object.  If  AB  =  10  feet;  CA  =  5  feet; 
B  D  =  25  feet,  find  DE. 

Have  pupils  find  other  methods  of  measurements  involving  the  use  of 
similar  triangles. 


^>.a.xA,o#vX^ 


338 


EIGHTH  YEAR 
n.    CONES  AND  PYRAMIDS 


A  pyramid  is  a  solid  having  for  its  base  a  triangle,  rectangle 
or  other  polygon,  and  having  for  its  lateral  faces  triangles 
meeting  at  a  point  called  the  vertex. 


Triangular  Pyramid  Quadrangular  Pyramid 


Cone 


A  cone  is  a  solid  having  for  its  base  a  circle,  and  bounded  by 
a  curved  surface  tapering  uniformly  to  a  point  called  the  apex. 

Construct  a  hollow  quadrangular  prism  out  of  cardboard. 
Construct  a  hollow  quadrangular  pyramid  with  a  base  aiid 
altitude  equal  to  the  base  and  altitude  of  the  prism.  Fill  the 
pyramid  with  sand  and  see  how  many  times  it  must  be  emptied 
into  the  prism  to  fill  it.  You  will  find  that  it  takes  3  pyramids 
full  of  sand  to  fill  the  prism.  The  volume  of  the  prism  is  equal 
to  the  product  of  the  area  of  the  base  times  the  altitude.  The 
volume  of  a  pyramid  is  ^  of  the  product  of  the  area  of  the  base 
times  the  altitude.  In  the  same  way  it  can  be  shown  that  the 
volumes  of  a  cone  is  one-third  of  the  volume  of  a  cylinder  of  the 
same  base  and  altitude. 

PRINCIPLE:  The  volume  of  a  pyramid  or  of  a  cone  is  equal  to 
one-third  of  the  product  of  the  area  of  the  base  times  its 
altitude. 

Exercise  6 

,  1.  What  is  the  volume  of  a  cone  having  a  base  7  inches  in 
diameter  and  a  height  of  9  inches?    Solution: 

3.5X3.5X9X3.1416 
Volume = g 


SPHERES 


339 


2.  Find  the  volume  of  a  pyramid  having  a  base  of  64  square 
feet  and  an  altitude  of  6  feet. 

3.  A  marble  cylindrical  shaft  1  foot  in  diameter  and  10  feet 
high  is  capped  by  a  marble  cone  having  the  same  diameter 
at  the  base.  The  altitude  of  the  cone  is  equal  to  its  diameter. 
Find  the  volume  of  the  shaft  and  cone. 

4.  The  Pyramid  of  Khufu,  in  Egypt,  has  a  square  base, 
measuring  750  feet  on  each  side,  and  its  height  was  originally 
482  feet.  Find  in  cubic  yards  its  contents  as  originally  com- 
pleted, according  to  these  figures. 

A  globe  or  sphere  is  a  solid  bounded  by  an  evenly  curved 
surface  every  point  of  which  is  equally  distant  from  a  point 
within  called  the  center. 

III.     SPHERES 

A  cubical  block  of  wood  may  be  made 
into  a  sphere  having  its  diameter  equal 
to  the  width  of  the  cube.  The  wood  that 
is  removed  lies  chiefly  at  the  corners  and 
along  the  edges  of  the  cube.  If  very 
exact  weights  are  made  of  the  cube  and 
of  the  sphere,  the  sphere  will  be  found  to 
weigh  .5236  as  much  as  the  cube.  Since 
the  volume  of  the  cube  is  equal  to  the  cube  of  its  edge  and  the 
diameter  of  the  sphere  is  equal  to  the  edge  of  the  cube. 

PRINCIPLE:    The  volume  of  a  sphere  is  equal  to  .5236  times 
the  cube  of  its  diameter. 
[See  page  243.] 

Exercise  6 

1.  Find  the  volume  of  a  sphere  4  inches  in  diameter. 

Solution:  .5236X  (4X4X4)  =  33.5104,  number  of  cubic 
inches  in  volume  of  sphere. 


340  EIGHTH  YEAR 

2.  Find  the  volume  of  a  sphere  6  inches  in  diameter. 

3.  If  the  earth  were  a  perfect  sphere  exactly  8000  miles 
in  diameter,  what  would  be  its  volume  in  cubic  miles? 

4.  A  globe  3  feet  in  diameter  is  how  many  times  the  size  of 
a  globe  1  foot  in  diameter? 

5.  A  wood  turner  makes  a  wooden  ball  3  inches  in  diameter 
from  a  3-inch  cube.  What  part  of  the  wood  is  wasted  in  making 
the  ball? 

6.  Measure  the  circumference  of  a  regulation  baseball. 
Find  its  diameter.  How  many  cubic  inches  are  there  in  the 
volume  of  the  baseball? 

Surface  of  a  Sphere 

If  a  croquet  ball  be  sawed  into  two  equal  parts  and  cord  be 
wrapped  around  the  curved  surface  and  then  around  one  of  the 
flat  circular  surfaces  where  the  ball  was  sawed,  it  is  found 
that  it  requires  twice  as  much  twine  for  the  curved  surface  of 
one  of  the  halves  as  for  the  circle.  It  therefore  requires  four 
times  as  much  cord  for  the  whole  surface  of  the  sphere  as  a 
circle  of  the  same  diameter.  Since  the  area  of  r.  circle  =  Trr^, 
•the  area  of  the  surface  of  a  sphere =47rr^ 

7.  Find  the  surface  of  a  sphere  8  inches  in  diameter. 
Solution:    Area  of  surface  of  a  sphere  =  47rr2. 

47rr2  =  4X3.1416X(4X4)  =201.0624. 
The  area  of  the  surface  of  this  sphere =201.0624  sq.  in. 

8.  Find  the  surface  of  a  sphere  5  inches  in  diameter;  6  inches 
in  diameter;  10  inches  in  diameter. 

9.  The  radius  of  the  earth  is  approximately  4000  miles. 
Find  the  approximate  number  of  square  miles  in  the  earth's 
surface. 

10.  Find  the  number  of  square  inches  of  leather  in  a  regu- 
lation baseball  cover.  (Use  measurements  found  for  Problem  6.) 


EQUATIONS  341 

IV.    SIMPLE  EQUATIONS 

Exercise  1 

An  equation  is  a  statement  of  the  equality  of  two  quantities. 
For  convenience  in  writing  equations,  letters  are  generally 
used  to  stand  for  the  unknown  numbers. 

For  example,  if  we  wish  to  solve  the  following  problem,  we 
will  find  it  convenient  to  use  an  equation: 

1.  A  newsboy  sold  twice  as  many  papers  today  as  he  did 
yesterday.  During  the  two  days  he  sold  96  papers.  How 
many  did  he  sell  each  day? 

We  may  let  the  letter  X  stand  for  the  unknown  number  of  papers  sold 
yesterday.    Then  2X  stands  for  the  number  of  papers  sold  today. 
X+2X  =  the  total  number  sold. 
But  96  =  the  total  number  sold 
Therefore  X+2X  =  96. 
or3X=96. 
The  expression  3X=96  is  an  equation  because  it  is  a  statement  of  the 
equaUty  of  3X  and  the  number  96. 

If  3X=96,  X  =  96-^3,  or  32. 
and2X=2X32,  or64. 

Solve  the  following  problems  by  using  equations: 

2.  A  farmer  bought  20  rods  of  chicken  wire  fencing.  He 
wished  to  make  a  lot  twice  as  long  as  it  was  wide.  Find  the 
number  of  rods  in  the  length  and  width  of  the  chicken  lot. 

Suggestion:  Let  X= the  number  of  rods  in  the  width.  Remember 
that  there  are  Jour  sides  to  be  considered  in  getting  the  perimeter  of  the 
lot. 

3.  Mary  is  twice  as  old  as  her  brother.  The  sum  of  their 
ages  is  21  years.    Find  the  age  of  each. 

4.  A  real  estate  dealer  bought  a  lot  on  which  he  built  a 
house  costing  three  times  as  much  as  the  lot.  If  the  total 
cost  of  the  house  and  lot  was  $5200,  what  was  the  cost  of  each? 


342  EIGHTH  YEAR 

5.  The  sum  of  three  numbers  is  84.  The  second  is  twice 
as  large  as  the  first  and  the  third  is  twice  as  large  as  the  second. 
Find  the  three  numbers. 

6.  A  farmer  has  a  farm  of  80  acres.  He  has  a  certain 
number  of  acres  in  oats;  twice  as  many  acres  in  pasture  and 
hay  as  in  oats;  and  five  times  as  many  acres  in  corn  as  in  oats. 
How  many  acres  has  he  in  each? 

7.  The  area  of  a  rectangle  is  56  square  inches  and  the 
width  is  4  inches.    Find  the  length. 

Let  X=the  length.    Then  4  times  X  or  4X=the  area. 

8.  The  area  of  a  field  is  80  square  rods.  The  length  is 
32  rods.  Find  the  width,  using  an  equation  as  shown  in  Prob- 
lem 7. 

Exercise  2 

As  shown  on  page  53,  an  equation  may  be  represented  by 
a  balance.  The  two  sides  will  therefore  balance  or  remain 
equal  if  we  take  the  same  quantity  or  number  from  both  sides 
or  if  we  add  the  same  numbers  to  both  sides. 

Suppose  we  wish  to  find  the  value  of  X  in  the  equation  X+6  =  19. 
If  we  take  away  6  from  the  left  side,  we  shall  have  left  merely  the  un- 
known number  X.  But  if  we  take  6  from  the  left  side,  we  must  also 
subtract  it  from  the  right  side  to  keep  both  sides  of  the  equation  equal  to 
each  other. 

X+6  =  19 
Subtracting:      6=6 

X  =  13 
If  we  wish  to  find  the  value  of  X  in  the  equation  X— 3  =  5,  we  must 
add  3  to  the  expression  X— 3  to  make  it  equal  to  X  because  X— 3  means 
three  less  than  X,  the  unknown  number.  If  we  add  3  to  the  left  side  of 
the  equation,  we  must  also  add  3  to  the  right  side  to  keep  both  sides  of 
the  equation  equal. 


EQUATIONS  343 

X-3=5 
Adding:      3=3 


X  =8 

Find  the  value  of  X  in  the  following  equations : 

1.  X+5  =  12.  11.    X+ll  =  15. 

2.  X-4=  9.  12.  3X-  5  =  13. 

3.  2X+3  =  17.  13.  5X+  2  =  27. 

4.  3X+1  =  10.  14.  2X-  6  =  12. 

5.  2X-2=  8.  16.    X-13  =  19. 

6.  5X+4  =  19.  16.  9X+  4  =  49. 

7.  2X-5  =  11.  17.  3X-  2=13. 

8.  X+7  =  15.  18.  4X+  3  =  21. 

9.  4X+3  =  19.  19.  7X-  5  =  16. 
10.  7X-3  =  11.  20.  5X+  6  =  26. 

Exercise  3 

1.  The  sum  of  two  consecutive  numbers  is  27.    What  are 
the  numbers? 

Suggestions:    Let  X  =  one  number.     Then  the  next  (consecutive)  num- 
ber is  X+1.    The  two  numbers  X+X+1  =27  or  2X+1  =27. 
Solve  the  equation  2X+1  =27  for  the  value  of  X. 

2.  John  is  4  years  older  than  Louise.     The  sum  of  their 
ages  is  24  years.    Find  their  ages. 

3.  Two  newsboys  made  45  cents  selling  papers.     One  made 
7  cents  more  than  the  other.     How  much  did  each  make? 

4.  A  farmer  bought  a  horse  and  a  cow  for  $185.    The  horse 
cost  $55  more  than  the  cow.     How  much  did  each  cost? 

6.  The  sum  of  two  numbers  is  80.    One  is  20  larger  than 
the  other.    Find  the  two  numbers. 

6.  A  lawyer  received  $26.60  for  collecting  a  debt  on  a 
commission  of  5%.    Find  the  amount  of  the  debt. 

Equation:    $26.60  =  .05  XX. 


344 


EIGHTH  YEAR 


Per  Cents  of  Food  Substances  in  the  Various 
American  Food  Products 


Protein 

Fat 

Carbo- 
hydrates 

Ash 
(mineral) 

Water 

Refuse 

White  bread 

9.2 

8  9 

9.8 

9.2 

16.7 

6.4 

1.0 

26.8 

3  3 

3.0 

2.5 

16.7 

16.5 

14.5 

13.7 

16.9 

3.2 

13.7 

16.1 

14.9 

6.0 

1.8 

1.4 

7.1 

7.0 

1.3 

1.4 

1,4 

0.9 

1.3 

0.7 

0.9 

0.7 

1.0 

0  4 

8  0 

0.4 

"o.'s 

0.8 
1.0 
0.7 
0.6 
0.5 
0,9 
0.2 
0.3 
1.9 
4.3 
2,3 

11.5 
8.6 
3.8 
6.6 
4,6 
5,8 
7.5 
5.2 

19,5 
6.9 

1.3 

1.8 

9.1 

1.9 

7.3 

1.2 

85.0 

35.3 

4.0 

.5 

18.5 

16.1 

7,8 

23.2 

25.5 

27.5 

2.1 

6,8 

18,4 

3,0 

1,3 

0,1 

0,6 

0.7 

0.5 

0.1 

0.2 

0,3 

0.1 

0.4 

0,2 

0,4 

0.2 

0.2 

0.4 

0.3 

0.1 

■"dVs 

0.4 
1.2 
0.5 
0.1 
0.4 
0,6 
0.1 

"2.5 

0.3 

3.0 

30.2 

33.7 

8.3 

4.9 

41,6 

25.5 

31.3 

33.3 

29.1 

26.6 

53.1 
52.1 
73.1 
75.4 
66  ..2 
77.9 

"3.3 
5.0 
4,8 
4.5 

"i.i 

4.3 

"'.4 

3.3 

14.7 

21.9 

22.0 

16.9 

7.7 

4,8 

8,9 

5,7 

10.8 

4.5 

3.9 

2.6 

2.5 

2.2 

.79.0 

88.0 

100.0 

70.0 

81.0 

96.0 

10.8 

14.3 

14.4 

5.9 

8.5 

12.7 

7.0 

2.7 

4.6 

70.6 

74.2 

68,5 

9.5 

3.5 

0.5 

45.9 

22,9 

4,3 

6,2 

6,2 

18.5 

6.8 

1.1 

1.5 
2.1 
1.0 
2.1 
.9 
3.0 
3,8 
0,7 
0.7 
0,5 
0,8 
0  7 
0.8 
0,7 
3,1 
1,3 
0,7 
0,8 
0,9 
1,1 
0,8 
0,9 
1,7 
1.0 
0.9 
0  9 
0,5 
0.6 
1.1 
0  4 
0.5 
0.4 
0.8 
0.4 
0.4 
0.1 

"0.3 
0.6 
0,4 
0,3 
0  4 
0,4 
0,6 
0.1 
0.3 
1.2 
2.4 
3.1 
1.1 
2,0 
0,4 
1.4 
1.1 
0.8 
1.1 
0.7 
1.5 
.6 

35.3 
35.7 

5.9 
12.5 

7.7 
13.6 
11.0 
30.8 
87.0 
91.0 
74.0 
51.7 
68.2 
50.3 
44,0 
50,7 
89.0 
45.4 
42.4 
52.9 
88.3 
62.6 
55.2 
68.5 
74.6 
70.0 
77.7 
78.9 
62.7 
66.4 
44.2 
94.3 
81.1 
80.5 
56.6 
12.3 
11.4 

63.3 

48.9 

58.0 

62.5 

63.4 

76  0 

85.9 

37.5 

44.8 

13.8 

18.8 

13.1 

2.7 

2.6 

.6 

21.1 

5  4 

1.4 

1.8 

1.4 

69 

1.0 

16.'4 
17.5 
14.3 
16.6 
3.3 

33.7 
22.7 
35.5 

20.0 
20.0 

20.0 
15.0 
10.0 
30.0 
20.0 
50.0 

15.0 
15.0 
40.0 

25'.0 
35.0 
25.0 
30.0 
27.0 
10.0 
5.0 
59.4 
50.0 
10.0 

io'.o 

45.0 
49.6 
86.4 
15.0 
25.0 
62.2 
52.4 
53.2 
24.5 
58.1 

Graham  bread 

Soda  crackers 

Corn  meal 

Oat  meal 

Buckwheat- 

Butter 

Cheese 

Milk 

Buttermilk 

Beef.  .  .. 

Veal 

Pork 

Sausage 

Turkey 

Fish 

Oysters 

Sweet  potatoes 

Peas.._ 

Beets 

Parsnips 

Lettuce 

Rice 

Sugar 

Grapes ...  . 

Oranges 

Pears    .... 

Figs — dried 

Filberts 

INDEX 


Addition 5, 6, 8, 9, 1 1, 18, 20-1 

Angles  and  lines 149,  150 

Applied  fraction  problems .  42,  45-8 

Applied  insurance  problems 121 

Applied  measurement  problems .  164 
Applied  percentage  problems. .  75-88 

Approximation  problems 196-8 

Banks  and  Banking 12^15 

Bank  checks 7201-3,  ^34-5 

checking  account 201 

deposit  sUp 200 

discount 208 

drafts 210-12,233 

federal  reserve 214-5 

organizing  a 213 

•     sight  and  time  drafts 210,  212 

issuing  notes 214 

review  problems 229-30 

savirigs  accounts 204 

Borrowing  money  at  bank  ....  207-8 

Bonds:... 221-4 

Book  making 168 

Boy  scouts 154 

Boys'  cash  account 136 

Business  forms 129-144 

invoices — bills 131 

monthly  statement 133 

cash  account 135-6 

daybook  and  journal 137 

personal  account 138-9 

inventory 140 

payroll 144 

cashiers'  memorandum 142 

receipts 134 

review  exercises 143,  146 

Business  transactions 89,  90 

By-products 79 

Calories 85-8 

Campfire  girls 287 

Clearance  sales 92 

Commissions 104-6,  192 

Cones  and  pyramids 338 

Coupons 223 

Cotton  industry 81-2 

Custom  duties 112 

Dairy  products 75-7 

Decimal  fractions 38-44 

Discounts 91-5, 193, 208 

Division  drills. 6,  7,  8,  10,  11,  18-25 
EflBciency  in  busmess 290-3 


Pages 

Efficiency  in  the  home 282-9 

budget 288-9 

cost  of  the  house 283-4 

expenses  of  the  home 286-7 

furnishing  the  home 284-0 

Electric  meter 302 

Equations 62-9,  241-3 

Equivalent  percents 50-3 

Exchange 209,  235 

Federal  reserve  banks 214 

Food  values 84-8,  344 

Foreign  money  and  travel .  .  .  .328-9 

Fractions — Common 27-48 

addition  of 29,  30 

division  of 34 

multiplication  of ... , 33 

subtraction  of 29,  30 

cancellation  of 33 

common  denominators 30 

mixed  numbers 31,  34,  184 

^>drills 37,45-48 

reviews 183 

Fractions — Decimals 38-44 

addition  of 40 

division  of 43 

multiphcation  of 41 

subtraction  of 40 

review  and  test  problems  . .  185-7 

Freight  and  express  rates 146 

Gardening 155 

Good  roads 272-6 

Graphs. 313-19 

{)ictorial 313 
ine 314 

bar 316 

distribution 318 

circle 319 

Insurance 118-124 

accident 124 

casualty 119 

fidelity 119 

fire 119 

life.. 122 

marine 119 

review 195 

Income  tax .116 

Indorsing  checks 202 

Interest 95-107 

compound 205-6 

notes 96 


345 


IIN  UEX — Continued 


Pages 

partial  payments 101-3 

six  percent  method 98 

table 100 

reviews 191 

Internal  revenue 115 

International  date  line 311 

International  money  orders 235 

Investments 225-8 

Irrigation 270-2 

Loaning  money 96,  207-8 

Longitude  and  Time 308-1 1 

Lumber  problems 278-9 

Making  change 26 

Measuring  instruments ....  294-307 

barometer 296 

hygrometer 297 

thermometer 294 

electric  meter 302 

<-as  meter 304-5 

steam  gauge 306 

surveyors  chain 307 

Metric  system 320-6 

table  of  capacity 824 

table  of  length 321 

table  of  square  measure 322 

table  of  volume 323 

table  of  weights 325 

Mixed  numbers 31,  35,  184 

MultipUcation  drills  jB,  7, 8, 10, 18-25 

Meat  industry 78-80 

National  expenses Ill 

National  revenues 112 

Paper  and  printing 165-170 

Parcel  post 144 

Percentage 49-88 

appUcation  of 89-90 

clearance  sales 92 

discounts 91-3 

equations 52,  61-65 

equivalent  percents 50 

factor  and  product 53-4 

problems  by  pupils 73 

reviews 71,  188,  193 

time  test  exercises 67-70 

"pi" 253 

Practical  measurements .  147-53, 

239-307 

circles 253,256-9 

cylinders 268 

hexagons 260 

paraflelograms     156 


Pages 

prisms 262 

quadrilaterals 151,  239 

rectangles 151,  240 

solids 261 

squares 141 

trapezoids •  .  . .  158 

triangles. . .  .  159-62,  240,  246,  335 

reviews 147,  240,  280-1 

volume 263-4 

Problems  by  a  farmer 277 

Pupils  own  problems 73 

Radiation 265-6 

Ratio  and  proportion 332 

Reading  and  writing  numbers . .  2,  3 

Reading  the  meter 302-3 

Remitting  money 231-8  * 

cabling 237 

checks ■ 234-5 

drafts 233 

emergency 236 

w^  express  money  order 232 

foreign  remittance 235 

postal  money  order 231 

telegraphing 236 

wireless 238 

Roman  notation 3 

Sales  slip 129 

Savings  accounts 204 

Shop  problems 255 

Short  methods  in  division 180 

Shortmethodsinm  ultipli  cation  1 76-8 

Signatures  and  seals 221 

Silos 269 

Speed  and  accuracy.  .  .  .5-11,  18-25 

tests 175-182 

Spheres 339 

Square  root 241-5 

Standard  time 309-11 

Stocks  and  bonds 216-230 

Subtraction  drills 174.^ 

Tariffs 113-5 

Taxes 107-10,  116-8 

special  assessments. .    110 

surtax  rates 117 

reviews 194 

Training  for  Efficiency 1,  171 

Trust  companies 215 

Type  sizes 167 

U.  S.  money 26 

Weather  reports 298-301 

Supplement 332-43 


I 


106 
C34eb 
1920a 


UNIVERSITY  OF  CALIFORNIA  AT  LOS  ANGELES 

THE  UNIVERSITY  LIBRARY 

TWs  book  is  DUE  on  the  last  date  stamped  below 


a  0  195^ 
KOV  5      1958 

DEO  4    1963 

Returnedl 
Col.  Lib,. 


8  1963 


HOVl  41963 


Form  1,-9 
Z0m-12,'39(3386> 


circles 253,  256-9 

cylinders 268 

hexagons 260 

parallelograms     156 


Type  sizes lUV 

U.  S.  money 26 

Weather  reports 298-301 

Supplement 332-43 


106 
C34eb 
1920a 


Mean  For  Mtanrlii  Bn 

Sitstticn:  * 


Quart 


Peck 
For  Meisarlng  Liquids: 

cm 


Pint 


Quart 


Scales 


TABLES  OP  DENOMlKAra  NUMBERS 

,  Dry  Measure       ^ 

2  pints =  1  quart (qt.l 

8  quarts =  1  peck (pk-M 

4  pecks =  1  bushel (bu.]| 

Liquid  Measure 

4  gills =  1  pint..... (pt.) 

2  pints =  1  quart (qt.) 

4  quarts =1  gallon (gal.) 

31^  gallons =  1  barrel (bbl.) 

63  gallons =  1  hogshead (hhd.) 

Avoirdupois  "Weight 

16  ounces  (oz.) =  1  pound (lb.) 

100  pounds =  1  hundredweight  (cwt.) 

2000  pounds =  1  ton (T.) 

One  pound  Avoirdupois  =7009  grains. 

Troy  Weight 

24  grains  (gr.) =  1  pennyweight  ....(pwt.) 

20  pennyweights =  1  ounce (oz.) 

12  ounces =1  pound (lb.) 

One  Pound  Troy =5760  grains. 

Apothecaries'  Weight 

60  grains  (gr.) =  1  dram (dr.orS) 

8  drams =  1  ounce (oz.  or  5) 

12  ounces .=1  pound (lb.  or  ft) 

One  Pound  Apothecaries*  weight =5760  grains 

Apothecaries'  Liquid  Measure 

60  minims  (m.) =  1  fluid  dram (5) 

8  fluid  drams =  1  fluid  ounce (5) 

16  fluid  ounces =  1  pint (fl.  oz.  or  O) 

8  pints =  1  gallon ^(cong.) 

Measure  of  Time 

60  seconds  (sec.) =  1  minute (min.) 

60  minutes =1  hour (hr.) 

24  hours =  1  day !...(da.) 

7  days =  1  week (wk.) 

365  days .'. =1  common  year (yr.) 

366  days =  I  leap  year 

■"All  schools  are  not  fully  equipped'  with  the  varioas 
measures  and  instruments  required  in  the  study  of 
Denominate  Numbers.  For  this  reason  suitable  illustrationa 
accompany  these  tables,  but  necessarily  reduced  In  size. 


C; 


t  QfCAUQTOBiail 


ICS 


JiSCt 


UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 


TABLES  OF  D 


A     000  992  284     o 


1 1  1    1. 

"Tl" 

1    1 1 1    1 

1    1 

1      1 

1       1 

1  1      1 

M    1  I  1    1  M  1  1  1  1 

O     1 

2 

3          4 

5 

6 
W- 

7 

8 

9          10     ^-11       .<. 

Foot  Rule,  reduced  to  one  third  of  its  true  length. 

ForMessuriDE  lingtiis:  _.  __ 

Linear  Meastire 


Surveyor's  Chain* 
Ftr  Sirfaei  Mcanrlir 

'j"'j"y"'j"'j"'j"'j"'. 
r.,f...r.i.f.i,f.i.r,i 


Carpenter's  Square 
niBtratlii  Stlids: 


Cube 


12  inches  (in.) =1  foot. 

3  feet =  1  yard (yd)^ 

5|  yards,  or  16|  feet ..  =  1  rod (rd.) 

40  rods =  1  furlong (fur.) 

320  rods,  or  5280  feet..  =  1  mile (mi.) 

Imi.  =320rd.  =1760  yd.  =5280  ft.  =63,360  in. 

Surveyors'  Linear  Measure 
7.92  inches  (in.) =1  link. -j. (1.) 


25 

100 

80 


links.... 
links.-, 
chains. 


=  1  rod (rd.) 

=  1  chain (ch.) 

=  1  mile (mi.) 


Square  Measure 
144  square  in.  (sq.  in.)..  =  1  square  foot  (sq.ft<) 

9  square  feet  (sq.ft.)  =1  square  yard  (sq.yd.) 
30^  sq.  yd.,or272^sq.ft  =  l  square  rod..(sq.rd.) 

160  square  rods =  1  acre (A.) 

640  acres =  1  square  mile  (sq.mi.) 

1  A.  =  160sq.rd.  =4340  sq.yd.  =43,560  sq.ft. 

Surveyors*  Square  Measure 

16  square  rods =  1  square  chain(sq.ch.) 

10  square  chains =  1  acre (A.) 

640  acres =1  square  mile  (sq.mi.) 

1  square  mile =  1  section (sec.) 

36  sections =  1  Cong,  township  (T.) 

Cubic  Measure 
1728  cubic  inches  (cu.in)  =1  cubic  foot....  (cu.ft.) 

27  cubic  feet =  1  cubic  yard.,  (cu.yd.) 

128  cubic  feet =1  cord (cd.) 

16  cubic  feet =  1  cord  foot (cd.ft.) 

8  cord  feet =  1  cord (cd.) 

*In8tead  of  the  standard  (Gunter's)  chain,  some  sur- 
veyors use  a  steel  tape  SO  feet  long,  divided  into  foot 
lengths,  each  of  these  being  marked  off  into  tenthr.  . 


^ 


